Question

A person observed the angle of elevation of the top of a tower as 30°. He walked 50 m towards the foot of the tower along level ground and found the angle of elevation of the top of the tower as 60°. Find the height of the tower.

Answer 1

Let be the tower of height. And person makes an angle of elevation of top of tower is 30°, he walks m towards the foot of tower then makes an angle of elevation 60°

Let , , and ,

Now we have to find height of tower.

We have the corresponding figure as follows

So we use trigonometric ratios.

In a triangle ABC,

Again in a triangle,

$$\begin{gathered} \Rightarrow \sqrt{3}h=\frac{h}{\sqrt{3}}+50 \\ \Rightarrow 3h=h+50\sqrt{3} \\ \Rightarrow 2h=50\sqrt{3} \\ \Rightarrow h=25\sqrt{3} \\ \Rightarrow h=25\times 1.73 \\ \Rightarrow h=43.25 \end{gathered}$$

Hence the height of tower is .