Question

A man 2 m tall, standing on top of a 25 m building observe the angle of depression of the top and bottom of the next building to be ${30}^{\circ }$ and ${60}^{\circ }$ respectively. The height of the next building is___m.

Answer 1

The diagram can be visualised as shown in the figure.

Let the height of next building be h.

In ΔADE, tan${30}^{\circ }$ = $\frac{(27-h)}{DE)}$

$\frac{1}{\sqrt{(}3)}$ = $\frac{(27-h)}{DE}$ ----------------------------- I

In ΔABC, tan${60}^{\circ }$= $\frac{27}{BC}$

$\sqrt{(}3)$ = $\frac{27}{BC)}$ ------------------------------II

DE = BC, so dividing I by II , we get

3 = $\frac{27}{(27-T)}$ $\Rightarrow$ h =18m