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

: We have been given the height of the tower, angle of elevation and hilltop as 60° and the angle of depression from the top of the tower of the foot of the hill as 30°. We need to find the height of the hill.

Let the height of the poles be ℎ. 

We know that for any angle θ $\tan \theta =\frac{\text{ pependicular }}{\text{ base }}$

In the ∆𝐴𝐵𝐶,

$\begin{array}{r}\tan {60}^{\circ }=\frac{h}{x}\\ \Rightarrow \sqrt{3}=\frac{h}{x}\\ \Rightarrow h=\sqrt{3}x\end{array}$

In ∆𝐸𝐷C

$\begin{array}{r}\tan {30}^{\circ }=\frac{h}{80-x}\\ \Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{80-x}\\ \Rightarrow h\sqrt{3}=80-x\end{array}$

Hence, the distance between poles is 20 𝑚 and 80 − 20 = 60 𝑚.