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Home » The upper part of a tree broken by wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of 380 30’ at a point 6 m from the foot of the tree. Calculate (i) the height at which the tree is broken. (ii) the original height of the tree correct to two decimal places.
The upper part of a tree broken by wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of 380 30’ at a point 6 m from the foot of the tree. Calculate (i) the height at which the tree is broken. (ii) the original height of the tree correct to two decimal places.
ML Agarwal Heights and distances class 10 Maths
The upper part of a tree broken by wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of 380 30’ at a point 6 m from the foot of the tree. Calculate (i) the height at which the tree is broken. (ii) the original height of the tree correct to two decimal places.

Consider TR as the total height of the tree

TP as the broken part which touches the ground at a distance of 6 m from the foot of the tree which makes an angle of 380 30’ with the ground

Take PR = x and TR = x + y

PQ = PT = y

In right triangle PQR

tan θ = PR/QR

Substituting the values

tan 380 30’ = x/6

x/6 = 0.7954

By cross multiplication

x = 0.7954 × 6 = 4.7724

We know that

sin θ = PR/PQ

Substituting the values

sin 380 30’ = x/y

So we get

0.6225 = 4.7724/y

y = 4.7724/0.6225 = 7.6665

Here

Height of the tree = 4.7724 + 7.6665 = 12.4389 = 12.44m

Height of the tree at which it is broken = 4.77 m

i

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