Question

From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60°. The pole subtends an angle 30° at the top of tower. Then the height of tower is ______.

Options

• `15sqrt(3)`

• `20sqrt(3)`

• `20 + 10sqrt(3)`

• 30

Answer 1

From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60°. The pole subtends an angle 30° at the top of tower. Then the height of tower is 30.

Explanation:

Let height of the tower PQ = y and distance between base of pole and base of tower = x

In ΔPQR, tan 60° = `(PQ)/(PR) = y/x`

⇒ `sqrt(3) = y/x`

⇒ y = `sqrt(3)`  ...(i)

In ΔQTS, tan 30° = `(QT)/(ST) = (y - 20)/x`

⇒ `1/sqrt(3) = (y - 20)/x`

⇒ y = `20 + x/sqrt(3)`

⇒ y = `20 + y/3`

⇒ `(2y)/3` = 20

⇒ y = 30 m.