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Class 10 › Mathematics › Some Applications of Trigonometry
CBSE2026Class Class 10 · Mathematics5 Marks · Long✅ Verified
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 distance of the point from the poles.
✅ Answer & Solution
Let height of poles $=h$, distance from 60° pole $=x$, from 30° pole $=(80-x)$.
$h=x\tan60°=x\sqrt3$
$h=(80-x)\tan30°=\frac{80-x}{\sqrt3}$
$$x\sqrt3=\frac{80-x}{\sqrt3} \Rightarrow 3x=80-x \Rightarrow 4x=80 \Rightarrow x=20$$
$$h=20\sqrt3\approx34.64\ m$$
Height of poles $\approx34.64$ m. Distance of point from poles: 20 m and 60 m.
