Q. 194.5( 8 Votes )

# If the angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°, then find the height of the cloud above the lake.

Answer :

**To find:**

The height of the cloud.

**Explanation:**

A is the position of the cloud, B is the point 200 m above the lake and F is the reflection in the lake.

Here AE = EF

EF = (m + 200) m

In ΔABC

BC = m cot 30° ……………….1

In Δ BCF

CF = 200 + m +200

= (400 + m) meters

BC = (400 + m) cot 60° ………………….2

From 1 and 2

m cot 30° = (400 + m) cot 60°

3 m = (400 + m)

m = 200 m

height above the cloud above the lake is (200 + 200) m = 400 m

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PREVIOUSAs observed from the top of a lighthouse, 200 m above the sea level, the angle of depression of a ship sailing towards it changes from 30° to 45°. Determine the distance travelled by the ship during the period of observation.NEXTTwo poles are ‘a’ metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then find the height of the smaller pole.

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