If the angle of elevation of a cloud from a point 10 metres above a lake is $30°$ and the angle of depression of its reflection in the lake is $60°$ , find the height of the cloud from the surface of lake.

$Cloud and its reflection in lake with angles 30° and 60°$

Question

If the angle of elevation of a cloud from a point 10 metres above a lake is

30°

and the angle of depression of its reflection in the lake is

60°

, find the height of the cloud from the surface of lake.

$Cloud and its reflection in lake with angles 30° and 60°$

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Accepted Answer

Step 1: Cloud C above lake, reflection C' below lake, observer O at 10m above lake surface, angles 30° and 60°
Step 2: $	an 30° = \frac{h}{x} \Rightarrow x = h\sqrt{3}$ ... (i)
Step 3: $	an 60° = \frac{h + 20}{x}$ ... (ii)
Step 4: Solving (i) and (ii): $h = 10$. $	herefore$ Height of cloud from surface of the lake $= 20$ m

Question

Solution