Question

An aeroplane flying at a height of 300 meters above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are ${60}^{}$ and ${45}^0$ respectively. Then the height of the lower plane from the ground, in meters is

• A. $100\sqrt{3}$
• B. $\frac{100}{\sqrt{3}}$
• C. 50
• D. 150 $(\sqrt{3}+1)$

Answer 1

The correct option is A $100\sqrt{3}$

$\tan {45}^0=\frac{h}{x}$
$\Rightarrow x=h$

$\tan {60}^0=\frac{300}{x}$

$\Rightarrow \sqrt{3}=\frac{300}{h}$

$\Rightarrow h=\frac{300}{\sqrt{3}}$

$\Rightarrow h=100\sqrt{3}m$