Question 144

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

Solution

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Angle of depression i.e. YCA = 45 degrees. This makes the angle of elevation from A to C i.e. CAX to be 45 degrees also.
This means that CX = AX and AX is equal to BD i.e. the horizontal distance between them.
CX becomes 75 m. XD = CD - CX ==> 160 - 75 = 85m.
Height of the first tower i.e. AB is equal to XD and thus the correct answer is Option A.

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