Question

The angles of elevation of a chiff at a point A on the ground and a point B 100 m vertically above A are ${60}^{\circ }$ and ${30}^{\circ }$ respectively. The height of cliff is

• A. $100\sqrt{3}m$
• B. $150\sqrt{3}m$
• C. 150 m
• D. $\frac{200}{\sqrt{3}}m$

Answer 1

Answer: (C)

150 m

REF.Image

Given Let 'h' be the height of cliff

Given

BD=100 m.

In $\Delta ABC$

$tan{60}^{\circ }=\frac{h}{AB}$

$AB=\frac{h}{\sqrt{3}}...\left(1\right)$

Now In $\Delta ECD$

$tan{30}^{\circ }=\frac{CE}{AB}=\frac{h-AE}{AB}\therefore =\frac{h-100}{AB}$

$\frac{1}{\sqrt{3}}=\frac{h-100}{AB}$

from eq (1)

$\frac{AB}{\sqrt{3}}=h=100\Rightarrow \frac{h}{3}=h-100$

$100=h-\frac{h}{3}\Rightarrow \frac{2h}{3}=100$

[h=150 m]

$\therefore$ Height of cliff is 150 m.