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

Question

From the top of a cliff 25 m high the angle of elevation of a top of tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is- (A) 25 m (B) 50 m (C) 75 m (D) 100 m

Tardigrade Admin · Accepted Answer

In triangle ABC tan α=(25/ x ) In triangle ADE tan α=( h -25/ x ) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a5446c3ac4b9b3d9e923f9bcd5769b95-.png" /> (25/x)=(h-25/x) ⇒ h=50 meter

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

25 m

50 m

75 m

100 m

In $△ A BC$
$tan α = \frac{25}{x}$
In $△ A D E$
$tan α = \frac{h - 25}{x}$

$\frac{25}{x} = \frac{h - 25}{x} \Rightarrow h = 50$ meter

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