Question

From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is

• A. 25m
• B. 50m
• C. 75m
• D. 100m

Answer 1

Answer: (B)

50m

Answer 2

Let AB be the cliff and CD be the tower
In $\triangle$OBC and OBD
$\angle$OBC = $\angle$OBD = $\theta$
OB is Common
BC = BD
So, the triangle is congruent
OC = OD = 25 m
Height of the tower = OC $+$ OD = 50 m.
So, the correct option is (B).