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Home » The angle of elevation of the top of a tower at a distance of from a point A on the ground is . If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at is , then find the height of the flagstaff [Use ]
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
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 ]

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 \mathrm{BAD}=60^{\circ}

Let C D=x

In \triangle \mathrm{ABC},

\tan 45^{\circ}=\frac{\mathrm{BC}}{\mathrm{AB}}

\Rightarrow 1=\frac{\mathrm{BC}}{120}

\Rightarrow \mathrm{BC}=120 \mathrm{~m}

=> in \triangle \mathrm{ABD},

\tan 60^{\circ}=\frac{\mathrm{BD}}{\mathrm{AB}}

\Rightarrow \sqrt{3}=\frac{\mathrm{BC}+\mathrm{CD}}{120}

\Rightarrow \mathrm{BC}+\mathrm{CD}=120 \sqrt{3}

\Rightarrow 120+\mathrm{x}=120 \sqrt{3}

\Rightarrow \mathrm{x}=120 \sqrt{3}-120

\Rightarrow \mathrm{x}=120(\sqrt{3}-1)

\Rightarrow \mathrm{x}=120(1.732-1)

\Rightarrow \mathrm{x}=120(0.732)

\Rightarrow \mathrm{x}=87.84 \approx 87.8 \mathrm{~m}

=> the height of the flagstaff is 87.8 \mathrm{~m}.

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