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An observer 1.6 m tall is 203 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:

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Question: An observer 1.6 m tall is 203 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:
[A].

21.6 m

[B].

23.2 m

[C].

24.72 m

[D].

None of these

Answer: Option A

Explanation:

Let AB be the observer and CD be the tower.

Draw BE CD.

Then, CE = AB = 1.6 m,

      BE = AC = 203 m.

DE = tan 30° = 1
BE 3
DE = 203 m = 20 m.
3

CD = CE + DE = (1.6 + 20) m = 21.6 m.

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