Question

The angle of elevation of top of a hill at the foot of a tower is 60 and the angle of depression from the top of tower to the foot of hill is 30. If tower is 50m high find the height of the high.

Answer 1

Let h be the height of the hill and x m be the distance between the foot of the hill and foot of the tower.

In rt.△ABC,

Cos 60° = x/h

x = h cot 60°........(i)

In rt.△DBC,

cot 30° = x/50

x = 50 cot 30°........(ii)

Equating (i) and (ii)

h cot 60° = 50 cot 30°

h = 50 cot 30°/cot 60°

h = 50 × √3/1√3 = 50 × 3 = 150 m

Therefore the height of the hill is 150 m.

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