The angle of elevation of a cloud from a point 60 m above a lake is 30°, and the angle of depression of its reflection in the lake is 60°. Find the height h of the cloud above the lake (in m). (The reflection is as far below the lake surface as the cloud is above it.)

Question

Accepted Answer

120. Let cloud height above lake = H, horizontal distance d. Elevation: tan30 = H-60/d. Depression of reflection: tan60 = H+60/d. Divide: tan60/tan30 = H+60/H-60 => 3 = H+60/H-60 => 3H-180 = H+60 => 2H = 240 => H = 120 m.

The angle of elevation of a cloud from a point 60 m above a lake is 30°, and the angle of depression of its reflection in the lake is 60°.
Find the height h of the cloud above the lake (in m). (The reflection is as far below the lake surface as the cloud is above it.)

Step-by-Step Solution

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More Class 10 Heights and Distances practice

The angle of elevation of a cloud from a point 60 m above a lake is 30°, and the angle of depression of its reflection in the lake is 60°.Find the height h of the cloud above the lake (in m). (The reflection is as far below the lake surface as the cloud is above it.)

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Heights and Distances practice

The angle of elevation of a cloud from a point 60 m above a lake is 30°, and the angle of depression of its reflection in the lake is 60°.
Find the height h of the cloud above the lake (in m). (The reflection is as far below the lake surface as the cloud is above it.)