Question

A man 2 m tall, standing on top of a 25 m building observes 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:

• A. 18 m
• B. 19 m
• C. 20 m
• D. 21 m

Answer 1

The correct option is A 18 m

The diagram can be visualised as shown in the figure.



Let the height of the 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

We know that, DE = BC and also by dividing II by I , we get,
$3=\frac{27}{27-h}$
$3\times (27-h)=27$
$h=18m$