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The horizontal distance between two towers is 150 m. The angle of depression of the top of one tower as observed from the top of the other tower, which is 120 m in height, is 30°. Find the height of the first tower.

Heights & Distances

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Answer

From figure,

FC = BD = 150 m.

The horizontal distance between two towers is 150 m. The angle of depression of the top of one tower as observed from the top of the other tower, which is 120 m in height, is 30°. Find the height of the first tower. Model Paper 3, Concise Mathematics Solutions ICSE Class 10.

In △AFC,

tan 30° = PerpendicularBase\dfrac{\text{Perpendicular}}{\text{Base}}

⇒13=AFFC⇒13=AF150⇒AF=1503=86.60 m.\Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{AF}{FC} \\[1em] \Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{AF}{150} \\[1em] \Rightarrow AF = \dfrac{150}{\sqrt{3}} = 86.60 \text{ m}.

From figure,

BF = AB - AF = 120 - 86.60 = 33.40 m

CD = BF = 33.40 meters.

Hence, height of first tower = 33.40 meters.

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