Question

From a point on the ground 30 m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. The height of the tower is ______.

Options

• 30 m

• `10sqrt(3)` m

• 10 m

• `30sqrt(3)` m

Answer 1

From a point on the ground, 30 m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. The height of the tower is `underlinebb(10sqrt(3) m)`.

Explanation:

Let AB be the tower and BC = 30 m be the ground such that ∠BCA = 30°.

Let AB = h metres.

Then, `(AB)/(BC) = tan 30^circ`

⇒ `h/30 = 1/sqrt(3)`

⇒ `h = 30/sqrt(3)`

⇒ `h = (30/sqrt(3) xx sqrt(3)/sqrt(3))`

⇒ `h = 10sqrt(3)`