Question

A man on the top of a cliff 100 m high, observe the angles of depression of two points on the opposite sides of the cliff as 30${}^o$ and 60${}^o$ respectively. Then, the distance between the two points is equal to

• A. $400\sqrt{3}m$
• B. $\frac{400}{\sqrt{3}}m$
• C. $\frac{100}{\sqrt{3}}m$
• D. $200\sqrt{3}m$

Answer 1

Answer: (B)

$\frac{400}{\sqrt{3}}m$

As shown n the figure, let $h$ be the height of the cliff.

$\tan {60}^o=\frac{100}{x}$

$\sqrt{3}=\frac{100}{x}$

$x=\frac{100}{\sqrt{3}}$

Similarly ,

$\tan {30}^o=\frac{100}{y}$

$\frac{1}{\sqrt{3}}=\frac{100}{y}$

$y=100\sqrt{3}$

Therefore,

$x+y=\frac{100}{\sqrt{3}}+100\sqrt{3}$

$x+y=\frac{400}{\sqrt{3}}m$

Hence option (B) is correct.