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:

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.