Mathematics
The horizontal distance between two towers is 75 m and the angular depression of the top of the first tower as seen from the top of the second, which is 160 m high, is 45°. Find the height of the first tower.
Heights & Distances
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Answer
Let AB be the first tower and CD be the second tower and ∠EDA = 45° is the angle of depression.
Given, angle of depression of the top of the first tower as seen from the top of the second tower is 45°.
We know that,
Alternate angles are equal.
∴ ∠DAF = ∠EDA = 45°.
From figure,
AF = BC = 75 m.
In △ADF,
From figure,
AB = FC = CD - DF = 160 - 75 = 85 m.
Hence, height of first tower = 85 m.
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