The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of depression from the top of the tower of the foot of the hill is 30°. If the tower is 50 m high, find the height of the hill.
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The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of depression from the top of the tower of the foot of the hill is 30°. If the tower is 50 m high, find the height of the hill.
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Step-by-step explanation:
Let AB be the tower and CD be the hill. Then, ∠ACB=30o,∠CAD=60o and AB=50 m.
Let CD=x m
In right △BAC, we have,
cot30o=ABAC
3=50AC
AC=503 m
In right △ACD, we have,
tan60o=ACCD
3=503x
x=50×3=150 m
Therefore, the height of the hill is 150 m.