Question

A helicopter is in a stationary position at a certain height over the lake. At a point 200 m above the surface of the lake, the angle of elevation of the helicopter is ${45}^{\circ }$. At the same time, the angle of depression of its reflection in the lake is ${75}^{\circ }$. Calculate the height of the helicopter from the surface of the lake:

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

Answer 1

The correct option is B $200\sqrt{3}m$

tan ${75}^{\circ }=\frac{(h+400)}{h}$
$h=200\times (\sqrt{3}-1)$
$h+200=200\sqrt{3}m$