Question

If the angle of elevation of a cloud from a point 200 metres above a lake is ${30}^{\circ }$ and the angle of depression of its reflection inthe lake is ${60}^{\circ }$ then the height of the cloud (n metres ) above the lake is

• A. 200
• B. 300
• C. 500
• D. None of these

Answer 1

The correct option is D None of these

Assumptions:

Let the dotted line represent the lake and pt A be the position of the cloud.

Pt. C is a point 200m above the lake.

To find:

Height of cloud from the dotted line (lake).

Solution:

In $\Delta ABC$
$\tan {30}^{\circ }=\frac{h}{x}$
x = $h\sqrt{3}$ .......(i)
In $\Delta BDC$
$\tan {60}^{\circ }=\frac{h+400}{x}$
$\sqrt{3}x=h+400$ .......(ii)
from (i) and (ii)
$h\sqrt{3}.\sqrt{3}=h+400$
3h - h = 400
h = $\frac{400}{2}=200$
h = 200
So, height of object above the lake = h + 200 = 200 + 200 = 400m