From the top of a cliff 20 m high

Asked by admin @ 23/08/2021 in Math viewed by 394 People

from the top of a cliff 20 m high the angle of elevation of top of Tower is found to be equal to the angle of depression of the foot of the tower find the height of the tower

Answered by admin @ 23/08/2021

The height of the tower is 40 m.

Step-by-step explanation:

Let the angle of elevation = angle of depression = θ

Let the cliff = AB

Tower = CD

Point E is corresponding to A i.e. 20 m from base D

In triangle ABD

tanФ = AB/BD

BD = AB/tanФ = 20/tanФ

AE = BD = 20/tanФ

In triangle AEC

tanФ = CE/AE

CE = AE x tanФ = 20/tanФ x tanФ = 20 m

Hence height of the tower = CD = CE + ED

= 20 + 20 = 40 meters.

Thus the height of the tower is 40 m.

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