Question

On the level ground, the angle of elevation of a tower is 30°. On moving 20 m nearer, the angle of elevation is 60°. The height of the tower is ______.

पर्याय

• 10 m

• `10sqrt(3)` m

• 15 m

• 20 m

Answer 1

On the level ground, the angle of elevation of a tower is 30°. On moving 20 m nearer, the angle of elevation is 60°. The height of the tower is `underlinebb(10sqrt(3)  m)`.

Explanation:

`x/h = cot 60^circ = 1/sqrt(3)`

⇒ `x = h/sqrt(3)`   ...(i)

`(x + 20)/h = cot 30^circ = sqrt(3)`

⇒ `x = (hsqrt(3) - 20)`   ...(ii)

∴ `h/sqrt(3) = (hsqrt(3) - 20)`

⇒ `h = 3h - 20sqrt(3)`

⇒ `2h = 20sqrt(3)`

⇒ `h = 10sqrt(3)`