Some Applications Of Trigonometry Archives

Some Applications Of Trigonometry

An observer $1.5 \mathrm{~m}$ tall is $28.5$ away from a tower and the angle of elevation of the top of the tower from the eye of the observer is $45^{\circ}$ . The height of the tower is (a) $27 \mathrm{~m}$ (b) $30 \mathrm{~m}$ (c) $28.5 \mathrm{~m}$ (d) None of these

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the observer and $\mathrm{CD}$ be the tower. Draw $\mathrm{BE} \perp \mathrm{CD}$, let $\mathrm{CD}=\mathrm{h}$ meters. Then, $\mathrm{AB}=1.5 \mathrm{~m},...

If the elevation of the sun changes from $30^{\circ}$ and $60^{\circ}$ then the difference between the lengths of shadows of a pole $15 \mathrm{~m}$ high, is (a) $7.5 \mathrm{~m}$ (b) $15 \mathrm{~m}$ (c) $10 \sqrt{3} \mathrm{~m}$ (d) $5 \sqrt{3} \mathrm{~m}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the pole and $\mathrm{AC}$ and $\mathrm{AD}$ be its shadows. $\angle \mathrm{ACB}=30^{\circ}, \angle \mathrm{ADB}=60^{\circ}$ and $\mathrm{AB}=15 \mathrm{~m}$ In $\triangle...

From the top of a hill, the angles of depression of two consecutive $\mathrm{km}$ stones due east are found to be $30^{\circ}$ and $45^{\circ}$ . The height of the hill is (a) $(\sqrt{3}+1) \mathrm{km}$ (b) $(3+\sqrt{3}) \mathrm{km}$ (c) $\frac{1}{2}(\sqrt{3}+1) \mathrm{km}$ (d) $\frac{1}{2}(3+\sqrt{3}) \mathrm{km}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the hill making angles of depression at points $\mathrm{C}$ and $\mathrm{D}$ such that $\angle \mathrm{ADB}=45^{\circ}, \angle \mathrm{ACB}=30^{\circ}$ and $\mathrm{CD}=1...

In a rectangle, the angle between a diagonal and a side of $30^{\circ}$ and the lengths of this diagonal is $8 \mathrm{~cm}$ . The area the rectangle is (a) $16 \mathrm{~cm}^{2}$ (b) $\frac{16}{\sqrt{3}} \mathrm{~cm}^{2}$ (c) $16 \sqrt{3} \mathrm{~cm}^{2}$ (d) $8 \sqrt{3} \mathrm{~cm}^{2}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{ABCD}$ be the rectangle in which $\angle \mathrm{BAC}=30^{\circ}$ and $\mathrm{AC}=8 \mathrm{~cm}$. In $\triangle \mathrm{BAC}$, we have: $\frac{\mathrm{AB}}{\mathrm{AC}}=\cos...

On the level ground, the angle of elevations of a tower is $30^{\circ}$ . On moving $20 \mathrm{~m}$ nearer, the angle of elevation is $60^{\circ}$ . The height of the tower is (a) $10 \mathrm{~m}$ (b) $10 \sqrt{3}$ (c) $15 \mathrm{~m}$ (d) $20 \mathrm{~m}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the tower and $\mathrm{C}$ and $\mathrm{D}$ be the points of observation such that $\angle \mathrm{BCD}=30^{\circ}, \angle \mathrm{BDA}=60^{\circ}, \mathrm{CD}=20 \mathrm{~m}...

If the angles of elevations of the top of a tower from two points at distances a and $b$ from the base and in the same straight line with it are complementary then the height of the tower is (a) $\sqrt{\frac{a}{b}}$ (b) $\sqrt{a b}$ (c) $\sqrt{a+b}$ (d) $\sqrt{\mathrm{a}-\mathrm{b}}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ be the tower and $C$ and $D$ bee the points of observation on $A C$. $\angle \mathrm{ACB}=\theta, \angle \mathrm{ADB}=90-\theta \text { and } \mathrm{AB}=\mathrm{hm}$ $A C=a, A D=b$ and $C...

The string of a kite is $100 \mathrm{~m}$ long and it makes an angle of $60^{\circ}$ with the horizontal. If there is no slack in the string, the height of the kite from the ground is (a) $50 \sqrt{3}$ (b) $100 \sqrt{3}$ (c) $50 \sqrt{2}$ (d) $100 \mathrm{~m}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the string of the kite and $\mathrm{AX}$ be the horizontal line. If $\mathrm{BC} \perp \mathrm{AX}$, then $\mathrm{AB}=100 \mathrm{~m}$ and $\angle \mathrm{BAC}=60^{\circ}$...

The angle of elevation of the top of a tower from the a point on the ground $30 \mathrm{~m}$ away from the foot of the tower is $30^{\circ}$ . The height of the tower is (a) $30 \mathrm{~m}$ (b) $10 \sqrt{3}$ (c) $20 \mathrm{~m}$ (d) $10 \sqrt{2}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the tower and $\mathrm{O}$ be the point of observation. $\angle \mathrm{AOB}=30^{\circ}$ and $\mathrm{OB}=30 \mathrm{~m}$ $\mathrm{AB}=\mathrm{h} \mathrm{m}$ In $\triangle...

The tops of two towers of heights $\mathrm{x}$ and $\mathrm{y}$ , standing on a level ground subtend angle of $30^{\circ}$ and $60^{\circ}$ respectively at the centre of the line joining their feet. Then $\mathrm{x}: \mathrm{y}$ is (a) $1: 2$ (b) $2: 1$ (c) $1: 3$ (d) $3: 1$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ and $C D$ be the two towers such that $A B=x$ and $C D=y$. We have, $\angle \mathrm{AEB}=30^{\circ}, \angle \mathrm{CED}=60^{\circ}$ and $\mathrm{BE}=\mathrm{DE}$ In $\triangle...

In the given figure, a tower $\mathrm{AB}$ is $20 \mathrm{~m}$ high and $\mathrm{BC}$ , its shadow on the ground is $20 \sqrt{3} \mathrm{~m}$ long. The sun’s altitude is (a) $30^{\circ}$ (b) $45^{\circ}$ (c) $60^{\circ}$ (d) None of these

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

SOLUTION: Let the sun's altitude be $\theta$. $\mathrm{AB}=20 \mathrm{~m}$ and $\mathrm{BC}=20 \sqrt{3} \mathrm{~m}$ In $\triangle \mathrm{ABC}$, $\tan \theta=\frac{\mathrm{AB}}{\mathrm{BC}}$...

A pole casts a shadow of length $2 \sqrt{3} \mathrm{~m}$ on the ground when the sun’s elevation is $60^{\circ}$ . The height of the pole is (a) $4 \sqrt{3}$ (b) $6 \mathrm{~m}$ (c) $12 \mathrm{~m}$ (d) $3 \mathrm{~m}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the pole and $\mathrm{BC}$ be its shadow. $\mathrm{BC}=2 \sqrt{3} \mathrm{~m}$ and $\angle \mathrm{ACB}=60^{\circ}$ In $\triangle \mathrm{ABC}$, $\tan...

The length of a vertical rod and its shadow are in the ratio $1: \sqrt{3}$ . The angle of elevation of the sun is (a) $30^{\circ}$ (b) $45^{\circ}$ (c) $60^{\circ}$ (d) $90^{\circ}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{A} \mathrm{B}$ be the rod and $\mathrm{BC}$ be its shadow; and $\theta$ be the angle of elevation of the sun. We have, $\mathrm{AB}: \mathrm{BC}=1: \sqrt{3}$ Let...

The length of the shadow of a tower standing on level ground is found to be $2 \mathrm{x}$ meter longer when the sun’s elevation is $30^{\circ}$ than when it was $45^{\circ}$ . The height of the tower is (a) $(2 \sqrt{3} x) m$ (b) $(3 \sqrt{2} \mathrm{x}) \mathrm{m}$ (c) $(\sqrt{3}-1) \times m$ (d) $(\sqrt{3}+1) \times \mathrm{m}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{CD}=\mathrm{h}$ be the height of the tower. $\mathrm{AB}=2 \mathrm{x}, \angle \mathrm{DAC}=30^{\circ}$ and $\angle \mathrm{DBC}=45^{\circ}$ In $\triangle \mathrm{BCD}$, $\tan...

If a $1.5 \mathrm{~m}$ tall girl stands at a distance of $3 \mathrm{~m}$ from a lamp post and casts a shadow of length $4.5 \mathrm{~m}$ on the ground, then the height of the lamp post is (a) $1.5 \mathrm{~m}$ (b) $2 \mathrm{~m}$ (c) $2.5 \mathrm{~m}$ (d) $2.8 \mathrm{~m}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the lamp post; $\mathrm{CD}$ be the girl and DE be her shadow. $\mathrm{CD}=1.5 \mathrm{~m}, \mathrm{AD}=3 \mathrm{~m}, \mathrm{DE}=4.5 \mathrm{~m}$ Let $\angle...

From the top of a cliff $20 \mathrm{~m}$ high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of the tower, The height of the tower is (a) $20 \mathrm{~m}$ (b) $40 \mathrm{~m}$ (c) $60 \mathrm{~m}$ (d) $80 \mathrm{~m}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ be the cliff and $C D$ be the tower. We have, $\mathrm{AB}=20 \mathrm{~m}$ $\text { Also, CE }=A B=20 \mathrm{~m}$ $\text { Let } \angle A C B=\angle C A E=\angle D A E=\theta$ $\text { In...

A kite is flying at a height of $30 \mathrm{~m}$ from the ground. The length of string from the kite to the ground is $60 \mathrm{~m}$ . A ssuming that there is no slack in the string, the angle of elevation of the kite at the ground is (a) $45^{\circ}$ (b) $30^{\circ}$ (c) $60^{\circ}$ (d) $90^{\circ}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let point A be the position of the kite and AC be its string We have, $\mathrm{AB}=30 \mathrm{~m}$ and $\mathrm{AC}=60 \mathrm{~m}$ Let $\angle \mathrm{ACB}=\theta$ In $\triangle \mathrm{ABC}$,...

The angle of depression of a car parked on the road from the top of a $150-\mathrm{m}$ . high tower is $30^{\circ}$ . The distance of the car from the tower is (a) $50 \sqrt{3}$ (b) $150 \sqrt{3}$ (c) $150 \sqrt{2}$ (d) 75 $\mathrm{m}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the tower and point $\mathrm{C}$ be the position of the car. $\mathrm{AB}=150 \mathrm{~m}$ and $\angle \mathrm{ACB}=30^{\circ}$ In $\triangle \mathrm{ABC}$, $\tan...

From a point on the ground, $30 \mathrm{~m}$ away from the foot of a tower, the angle of elevation of the top of the tower is $30^{\circ}$ . The height of the tower is (a) $30 \mathrm{~m}$ (b) $10 \sqrt{3}$ (c) $10 \mathrm{~m}$ (d) $30 \sqrt{3}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{A} \mathrm{B}$ be the tower and point $\mathrm{C}$ be the point of observation on the ground. We have, $\mathrm{BC}=30 \mathrm{~m}$ and $\angle \mathrm{ACB}=30^{\circ}$ In $\triangle...

A ladder $15 \mathrm{~m}$ long just reaches the top of a vertical wall. If the ladder makes an angle of $60^{\circ}$ with the wall then the height of the wall is (a) $15 \sqrt{3}$ (b) $\frac{15 \sqrt{3}}{2}$ (c) $\frac{15}{2}$ (d) $15 \mathrm{~m}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the wall and $\mathrm{AC}$ be the ladder $\mathrm{AC}=15 \mathrm{~m}$ and $\angle \mathrm{BAC}=60^{\circ}$ $\cos 60^{\circ}=\frac{\mathrm{AB}}{\mathrm{AC}}$ $\Rightarrow...

A ladder makes an angle of $60^{\circ}$ with the ground when placed against a wall. If the foot of the ladder is $2 \mathrm{~m}$ away from the wall, the length of the ladder is (a) $\frac{4}{\sqrt{3}}$ (b) $4 \sqrt{3}$ (c) $2 \sqrt{2} \mathrm{~m}$ (d) $4 \mathrm{~m}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ be the wall and $A C$ be the ladder. $\mathrm{BC}=2 \mathrm{~m}$ and $\angle \mathrm{ACB}=60^{\circ}$ In $\triangle A B C$, $\cos 60^{\circ}=\frac{\mathrm{BC}}{\mathrm{AC}}$ $\Rightarrow...

The shadow of a 5-m-long stick is $2 \mathrm{~m}$ long. At the same time, the length of the shadow of a $12.5-\mathrm{m}$ -high tree is (a) $3 \mathrm{~m}$ (b) $3.5 \mathrm{~m}$ (c) $4.5 \mathrm{~m}$ (d) 5 .

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ be a stick and $B C$ be its shadow, and $P Q$ be the tree and $Q R$ be its shadow. $\mathrm{AB}=5 \mathrm{~m}, \mathrm{BC}=2 \mathrm{~m}, \mathrm{PQ}=12.5 \mathrm{~m}$ In $\triangle...

If a pole of $12 \mathrm{~m}$ high casts a shadow $4 \sqrt{3}$ long on the ground then the sun’s elevation is (a) $60^{\circ}$ (b) $45^{\circ}$ (c) $30^{\circ}$ (d) $90^{\circ}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ be the pole, $B C$ be its shadow and $\theta$ be the sun's elevation. We have, $\mathrm{AB}=12 \mathrm{~m}$ and $\mathrm{BC}=4 \sqrt{3} \mathrm{~m}$ In $\triangle \mathrm{ABC}$, $\tan...

If the length of the shadow of a tower is $\sqrt{3}$ times its height then the angle of elevation of the sun is (a) $45^{\circ}$ (b) $30^{\circ}$ (c) $60^{\circ}$ (d) $90^{\circ}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ be the pole and $B C$ be its shadow. Let $A B=h$ and $B C=x$ such that $x=\sqrt{3}$ h (given) and $\theta$ be the angle of elevation. From $\triangle \mathrm{ABC}$, we have...

If the height of a vertical pole is equal to the length of its shadow on the ground, the angle of elevation of the sun is (a) $0^{\circ}$ (b) $30^{\circ}$ (c) $45^{\circ}$ (d) $60^{\circ}$

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ represents the vertical pole and $\mathrm{BC}$ represents the shadow on the ground and $\theta$ represents angle of elevation the sun. In $\triangle A B C$, $\tan...

From the top of a building AB, $60 \mathrm{~m}$ high, the angles of depression of the top and bottom of a vertical lamp post $\mathrm{CD}$ are observed to the $30^{\circ}$ and $60^{\circ}$ respectively. Find (iii) the difference between the heights of the building and the lamp post.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

$\mathrm{AB}=60 \mathrm{~m}, \angle \mathrm{ACE}=30^{\circ}$ and $\angle \mathrm{ADB}=60^{\circ}$ Let $\mathrm{BD}=\mathrm{CE}=\mathrm{x}$ and $\mathrm{CD}=\mathrm{BE}=\mathrm{y}$ $\Rightarrow...

From the top of a building AB, $60 \mathrm{~m}$ high, the angles of depression of the top and bottom of a vertical lamp post $\mathrm{CD}$ are observed to the $30^{\circ}$ and $60^{\circ}$ respectively. Find (i) The horizontal distance between $\mathrm{AB}$ and $\mathrm{CD}$ , (ii) the height of the lamp post,

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

$\mathrm{AB}=60 \mathrm{~m}, \angle \mathrm{ACE}=30^{\circ}$ and $\angle \mathrm{ADB}=60^{\circ}$ $\mathrm{BD}=\mathrm{CE}=\mathrm{x}$ and $\mathrm{CD}=\mathrm{BE}=\mathrm{y}$ $\Rightarrow...

An electrician has to repair an electric fault on a pole of height 4 meters. He needs to reach a point 1 meter below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use, which when inclined at an angle of $60^{\circ}$ to the horizontal would enable him to reach the required position?

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AC}$ be the pole and $\mathrm{BD}$ be the ladder We have, $\mathrm{AC}=4 \mathrm{~m}, \mathrm{AB}=1 \mathrm{~m}$ and $\angle \mathrm{BDC}=60^{\circ}$ And, $B C=A C-A B=4-1=3 m$ In...

From the top of a vertical tower, the angles depression of two cars in the same straight line with the base of the tower, at an instant are found to be $45^{\circ}$ and $60^{\circ}$ . If the cars are $100 \mathrm{~m}$ apart and are on the same side of the tower, find the height of the tower.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let OP be the tower and points A and B be the positions of the cars. $\mathrm{AB}=100 \mathrm{~m}, \angle \mathrm{OAP}=60^{\circ} \text { and } \angle \mathrm{OBP}=45^{\circ}$ $\text { Let } O P=h$...

A ladder of length 6meters makes an angle of $45^{\circ}$ with the floor while leaning against one wall of a room. If the fort of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of $60^{\circ}$ with the floor. Find the distance between two walls of the room.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ and $C D$ be the two opposite walls of the room and the foot of the ladder be fixed at the point $\mathrm{O}$ on the ground. $\mathrm{AO}=\mathrm{CO}=6 \mathrm{~m}, \angle...

The angle of elevation of the top of a tower from to points at distances of $4 \mathrm{~m}$ and $9 \mathrm{~m}$ from the base of the tower and in the same straight line with it are complementary. Show that the height of the tower is 6 meters.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ be the tower and $C$ and $D$ be two points such that $A C=4 \mathrm{~m}$ and $A D=9 m$. Let: $\mathrm{AB}=\mathrm{hm}, \angle \mathrm{BCA}=\theta$ and $\angle...

From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $30^{\circ}$ and $45^{\circ}$ respectively. If the bridge is at a height of $2.5 \mathrm{~m}$ from the banks, find the width of the river.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{A}$ and $\mathrm{B}$ be two points on the banks on the opposite side of the river and $\mathrm{P}$ be the point on the bridge at a height of $2.5 \mathrm{~m}$. $\mathrm{DP}=2.5, \angle...

As observed form the top of a lighthouse, $100 \mathrm{~m}$ above sea level, the angle of depression of a ship, sailing directly towards it, changes from $30^{\circ}$ and $60^{\circ}$ . Determine the distance travelled by the ship during the period of observation.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{OA}$ be the lighthouse and $\mathrm{B}$ and $\mathrm{C}$ be the positions of the ship. $\mathrm{OA}=100 \mathrm{~m}, \angle \mathrm{OBA}=30^{\circ}$ and $\angle \mathrm{OCA}=60^{\circ}$...

The angle of elevation of the top of a tower from ta point on the same level as the foot of the tower is $30^{\circ}$ . On advancing $150 \mathrm{~m}$ towards foot of the tower, the angle of elevation becomes $60^{\circ}$ Show that the height of the tower is $129.9$ metres.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ be the tower $\mathrm{CD}=150 \mathrm{~m}, \angle \mathrm{ACB}=30^{\circ}$ and $\angle \mathrm{ADB}=60^{\circ}$ $\mathrm{AB}=\mathrm{h} \mathrm{m}$ and $\mathrm{BD}=\mathrm{x} \mathrm{m}$...

The angle of elevation of an aeroplane from a point on the ground is $45^{\circ}$ after flying for 15 seconds, the elevation changes to $30^{\circ}$ . If the aeroplane is flying at a height of 2500 meters, find the speed of the areoplane.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let the height of flying of the aero-plane be $\mathrm{PQ}=\mathrm{BC}$ and point $\mathrm{A}$ be the point of observation. $\mathrm{PQ}=\mathrm{BC}=2500 \mathrm{~m}, \angle \mathrm{PAQ}=45^{\circ}$...

The angle of elevation of the top $Q$ of a vertical tower $P Q$ from a point $X$ on the ground is $60^{\circ}$ . At a point $Y, 40 \mathrm{~m}$ vertically above $\mathrm{X}$ , the angle of elevation is $45^{\circ}$ . Find the height of tower PQ.

CBSE, Class 10, RS Aggarwal, Some Applications Of Trigonometry

$\mathrm{XY}=40 \mathrm{~m}, \angle \mathrm{PXQ}=60^{\circ}$ and $\angle \mathrm{MYQ}=45^{\circ}$ Let $P Q=h$ $\mathrm{MP}=\mathrm{XY}=40 \mathrm{~m},...

A man on the deck of a ship, $16 \mathrm{~m}$ above water level, observe that that angle of elevation and depression respectively of the top and bottom of a cliff are $60^{\circ}$ and $30^{\circ} .$ Calculate the distance of the cliff from the ship and height of the cliff.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ be the deck of the ship above the water level and $D E$ be the cliff. $\mathrm{AB}=16 \mathrm{~m}$ such that $\mathrm{CD}=16 \mathrm{~m}$ and $\angle \mathrm{BDA}=30^{\circ}$ and $\angle...

The angles of depression of the top and bottom of a tower as seen from the top of a $60 \sqrt{3} \mathrm{~m}$ high cliff are $45^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let AD be the tower and $\mathrm{BC}$ be the cliff. $\mathrm{BC}=60 \sqrt{3}, \angle \mathrm{CDE}=45^{\circ}$ and $\angle \mathrm{BAC}=60^{\circ}$ Let $\mathrm{AD}=\mathrm{h}$ $\Rightarrow...

The angle of elevation of the top of a vertical tower from a point on the ground is $60^{\circ}$ . From another point $10 \mathrm{~m}$ vertically above the first, its angle of elevation is $30^{\circ}$ . Find the height of the tower.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{PQ}$ be the tower $\mathrm{AB}=10 \mathrm{~m}, \angle \mathrm{MAP}=30^{\circ}$ and $\angle \mathrm{PBQ}=60^{\circ}$ $M Q=A B=10 \mathrm{~m}$ Let $B Q=x$ and $P Q=h$ => $A M=B Q=x$...

The angle of depression form the top of a tower of a point A on the ground is $30^{\circ}$ . On moving a distance of 20 meters from the point A towards the foot of the tower to a point $B$ , the angle of elevation of the top of the tower to from the point $\mathrm{B}$ is $60^{\circ}$ . Find the height of the tower and its distance from the point $\mathrm{A}$ .

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{PQ}$ be the tower. $\mathrm{AB}=20 \mathrm{~m}, \angle \mathrm{PAQ}=30^{\circ}$ and $\angle \mathrm{PBQ}=60^{\circ}$ Let $B Q=x$ and $P Q=h$ In $\triangle \mathrm{PBQ}$, $\tan...

From the top of a 7 meter high building, the angle of elevation of the top of a cable tower is $60^{\circ}$ and the angle of depression of its foot is $45^{\circ}$ . Determine the height of the tower.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the $7-\mathrm{m}$ high building and $\mathrm{CD}$ be the cable tower, $\mathrm{AB}=7 \mathrm{~m}, \angle \mathrm{CAE}=60^{\circ}, \angle \mathrm{DAE}=\angle...

The angle of elevation of the top of a chimney form the foot of a tower is $60^{\circ}$ and the angle of depression of the foot of the chimney from the top of the tower is $30^{\circ}$ . If the height of the tower is 40 meters. Find the height of the chimney.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{PQ}$ be the chimney and $\mathrm{AB}$ be the tower. $\mathrm{AB}=40 \mathrm{~m}, \angle \mathrm{APB}=30^{\circ}$ and $\angle \mathrm{PAQ}=60^{\circ}$ In $\triangle \mathrm{ABP}$, $\tan...

The horizontal distance between two towers is 60 meters. The angle of depression of the top of the first tower when seen from the top of the second tower is $30^{\circ}$ . If the height of the second tower is 90 meters. Find the height of the first tower.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{DE}$ be the first tower and $\mathrm{AB}$ be the second tower. => $\mathrm{AB}=90 \mathrm{~m}$ and $\mathrm{AD}=60 \mathrm{~m}$ such that $\mathrm{CE}=60 \mathrm{~m}$ and $\angle...

The angle of elevation on the top of a building from the foot of a tower is $30^{\circ}$ . The angle of elevation of the top of the tower when seen from the top of the second water is $60^{\circ}$ .If the tower is $60 \mathrm{~m}$ high, find the height of the building.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be thee building and $\mathrm{PQ}$ be the tower. $\mathrm{PQ}=60 \mathrm{~m}, \angle \mathrm{APB}=30^{\circ}, \angle \mathrm{PAQ}=60^{\circ}$ In $\triangle \mathrm{APQ}$, $\tan...

A TV tower stands vertically on a bank of canal. Form a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60^{\circ}$ . From another point $20 \mathrm{~m}$ away from the point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is $30^{\circ}$ . Find the height of the tower and the width of the canal.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{PQ}=\mathrm{h} \mathrm{m}$ be the height of the $\mathrm{TV}$ tower and $\mathrm{BQ}=\mathrm{x} \mathrm{m}$ be the width of the canal. We have, $\mathrm{AB}=20 \mathrm{~m}, \angle...

A straight highway leads to the foot of a tower, A man standing on the top of a the tower observe c car at an angle of depression of $30^{\circ}$ which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be $60^{\circ}$ . Find the time taken by the car to reach the foot of the tower form this point.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{PQ}$ be the tower: $\angle \mathrm{PBQ}=60^{\circ}$ and $\angle \mathrm{PAQ}=30^{\circ}$ Let $P Q=h, A B=x$ and $B Q=y$ In $\triangle \mathrm{APQ}$, $\tan...

From the point of a tower $100 \mathrm{~m}$ high, a man observe two cars on the opposite sides to the tower with angles of depression $30^{\circ}$ and $45^{\circ}$ respectively. Find the distance between the cars

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{PQ}$ be the tower $\mathrm{PQ}=100 \mathrm{~m}, \angle \mathrm{PQR}=30^{\circ}$ and $\angle \mathrm{PBQ}=45^{\circ}$ In $\triangle \mathrm{APQ}$ $\tan...

Two men are on opposite side of tower. They measure the angles of elevation of the top of the tower as $30^{\circ}$ and $45^{\circ}$ respectively. If the height of the tower is 50 meters, find the distance between the two men.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $C D$ be the tower and $A$ and $B$ be the positions of the two men standing on the opposite sides. $\angle \mathrm{DAC}=30^{\circ}, \angle \mathrm{DBC}=45^{\circ} \text { and } \mathrm{CD}=50...

Two poles of equal heights are standing opposite to each other on either side of the road which is $80 \mathrm{~m}$ wide, From a point $\mathrm{P}$ between them on the road, the angle of elevation of the top of one pole is $60^{\circ}$ and the angle of depression from the top of another pole at $P$ is $30^{\circ}$ . Find the height of each pole and distance of the point $\mathrm{P}$ from the poles.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ and $C D$ be the equal poles; and BD be the width of the road. $\angle \mathrm{AOB}=60^{\circ}$ and $\angle \mathrm{COD}=60^{\circ}$ In $\triangle \mathrm{AOB}$, $\tan...

On a horizonal plane there is a vertical tower with a flagpole on the top of the tower. At a point, 9 meters away from the foot of the tower, the angle of elevation of the top and bottom of the flagpole are $60^{\circ}$ and $30^{\circ}$ respectively. Find the height of the tower and the flagpole mounted on it

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{OX}$ be the horizontal plane, AD be the tower and $\mathrm{CD}$ be the vertical flagpole We have: $\mathrm{AB}=9 \mathrm{~m}, \angle \mathrm{DBA}=30^{\circ}$ and $\angle...

The angle of elevation of the top of an unfinished tower at a distance of $75 \mathrm{~m}$ from its base is $30^{\circ} .$ How much higher must the tower be raised so that the angle of elevation of its top at the same point may be $60^{\circ}$ .

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the unfinished tower, $\mathrm{AC}$ be the raised tower and $\mathrm{O}$ be the point of observation We have: $\mathrm{OA}=75 \mathrm{~m}, \angle \mathrm{AOB}=30^{\circ}$ and...

A statue $1.46 \mathrm{~m}$ tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the status is $60^{\circ}$ and from the same point, the angle of elevation of the top of the pedestal is $45^{\circ}$ . Find the height of the pedestal.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AC}$ be the pedestal and $\mathrm{BC}$ be the statue such that $\mathrm{BC}=1.46 \mathrm{~m}$. We have: $\angle \mathrm{ADC}=45^{\circ}$ and $\angle \mathrm{ADB}=60^{\circ}$...

The vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height $6 \mathrm{~m}$ . At a point on the plane, the angle of elevation of the bottom of the flagstaff is $30^{\circ}$ and that of the top of the flagstaff $60^{\circ}$ . Find the height of the tower

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{AB}$ be the tower and $\mathrm{BC}$ be the flagstaff, $\mathrm{BC}=6 \mathrm{~m}, \angle \mathrm{AOB}=30^{\circ}$ and $\angle \mathrm{AOC}-60^{\circ}$ Let $A B=h$ In $\triangle...

From a point on the ground $40 \mathrm{~m}$ away from the foot of a tower, the angle of elevation of the top of the tower is $30^{\circ}$ . The angle of elevation of the top of a water tank (on the top of the tower) is $45^{\circ}$ , Find (i) the height of the tower, (ii) the depth of the tank.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{BC}$ be the tower and $\mathrm{CD}$ be the water tank. $\mathrm{AB}=40 \mathrm{~m}, \angle \mathrm{BAC}=30^{\circ}$ and $\angle \mathrm{BAD}=45^{\circ}$ In $\triangle \mathrm{ABD}$,...

The angle of elevation of the top of a tower at a distance of $120 \mathrm{~m}$ from a point A on the ground is $45^{\circ}$ . If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at $\mathrm{A}$ is $60^{\circ}$ , then find the height of the flagstaff [Use $\sqrt{3}=1.732$ ]

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $\mathrm{BC}$ and $\mathrm{CD}$ be the heights of the tower and the flagstaff, respectively. We have, $\mathrm{AB}=120 \mathrm{~m}, \angle \mathrm{BAC}=45^{\circ}, \angle...

The angles of elevation of the top of a tower from two points at distance of 5 metres and 20 metres from the base of the tower and is the same straight line with it, are complementary. Find the height of the tower.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let the height of the tower be $\mathrm{AB}$. $\mathrm{AC}=5 \mathrm{~m}, \mathrm{AD}=20 \mathrm{~m}$ Let the angle of elevation of the top of the tower (i.e. $\angle \mathrm{ACB})$ from point...

An observer $1.5 \mathrm{~m}$ tall is 30 away from a chimney. The angle of elevation of the top of the chimney from his eye is $60^{\circ}$ . Find the height of the chimney.

CBSE, Class 10, Maths, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $C E$ and AD be the heights of the observer and the chimney, respectively. We have, $\mathrm{BD}=\mathrm{CE}=1.5 \mathrm{~m}, \mathrm{BC}=\mathrm{DE}=30 \mathrm{~m}$ and $\angle...

A kite is flying at a height of 75 in from the level ground, attached to a string inclined at $60^{\circ}$ . to the horizontal. Find the length of the string, assuming that there is no slack in it.

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

$\mathrm{OX}$ be the horizontal ground and $\mathrm{A}$ be the position of the kite. let $\mathrm{O}$ be the position of the observer and $\mathrm{OA}$ be the thread. draw $\mathrm{AB} \perp...

A tower stands vertically on the ground. From a point on the ground which is $20 \mathrm{~m}$ away from the foot of the tower, the angle of elevation of its top is found to be $60^{\circ}$ . Find the height of the tower. [Take $\sqrt{3}=1.732$ ]

CBSE, Class 10, Maths, RS Aggarwal, Some Applications Of Trigonometry

Let $A B$ be the tower standing vertically on the ground and 0 be the position of the obsrever we now have: $\mathrm{OA}=20 \mathrm{~m}, \angle \mathrm{OAB}=90^{\circ}$ and $\angle...

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Let us assume that, AB be the tower. Let C and D be the two points that are 4 and 9 metres away from the base, respectively. As per question, In right angle ΔABC, AB/BC = tan x AB/4 = tan...

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Let the tower be AB. The initial position and final position of the car be D and C respectively. Since the man is at the top of the tower, as a result the angles...

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30° (see Fig. 9.13). Find the distance travelled by the balloon during the interval.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Let the balloon’s initial position be A and final position be B. Balloon’s height above the girl height = 88.2 m – 1.2 m = 87 m. To Calculate: The distance travelled by the balloon = DE =...

As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: The lighthouse AB height is 75 m. And let C and D be the positions of the ships. The angles of depression from the lighthouse are 30° and 45° . Draw a figure based on given instructions:...

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Let the height of the building i.e. AB be 7 m and the height of the tower be EC. A is the point where the tower's elevation is 60 degrees and the angle of depression of its foot is...

A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joing this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Provided that, AB is the height of the tower. DC = 20 m (given here) As per figure given, In right angle ΔABD, AB/BD = tan 30° AB/(20+BC) = 1/√3 AB = (20+BC)/√3 … (i) Again, In right angle...

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Let AB and CD be poles with equal-height. O is the point between them where the elevation height is measured. The distance between the poles is denoted by BD. AB = CD, as seen in the...

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Let CD be the tower's height. AB be the building's height. The distance between the building's foot and the tower be BC. From the tower and the building, the elevation is 30...

A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Let AB be the height of statue. The elevation is taken from D, which is a point on the ground. To Calculate: Height of pedestal = BC = AC-AB From the figure above, In right angle ΔBCD,...

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Let BC be the 20 meter high building. The elevation is taken from D, which is a point on the ground. Transmission tower’s height = AC – BC = AB We need to find: The height of the tower...

A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Let the boy to stand initially at point Y with a 30° inclination before approaching the building at point X with a 60° inclination. To Find: XY i.e. the distance walked by the boy...

A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Draw a figure based on the instructions provided, Let BC be the height of the kite from the ground, i.e., BC = 60 m Inclined length of the string from the ground = AC, and A is the point...

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Let AB be the tower's height, and C be the point elevation 30 metres away from the tower's foot. We need to Find: AB, which is the height of the tower In right angle triangle ABC AB/BC =...

A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: According to the contractor's plan, Let ABC be a 30° inclined slide with length AC, and PQR be a 60° inclined slide with length PR. We need to Find: AC and PR In right angle ΔABC, AB/AC =...

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: Draw a figure based on the given instructions. Let AC be the tree's broken branch. C = 30° BC = 8 m We need to Find: AB, which is height of the tree, From figure: The sum of AB and...

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°. (see fig. 9.11)

CBSE, Class 10, Maths, NCERT, Some Applications Of Trigonometry

Solution: The rope is 20 metres long and makes a 30° angle with the ground level. Given here: Measure of AC = 20 m and measure of angle C = 30° We need to Find: Height of the pole Let the...