Question

From the top of a 50 m high tower, the angles of depression of the top and bottom of a pole are observed to be 45° and 60° respectively. Find the height of the pole.

Answer 1

Let H be the height of the pole, makes an angle of depression from the top of the tower to top and bottom of\ poles are 45° and 60° respectively.

Let AB = H, CE = h, AD = x and DE = 50 m.

∠CBE = 45° and ∠DAE = 60°

Here, we have to find height of pole.

The corresponding figure is as follows

In ΔADE

⇒ `tan A = (DE)/(AD)`

⇒ `tan 60^circ = 50/x`

⇒ `x = 50/sqrt(3)`

Again in ΔBCE

⇒ `tan B = (CE)/(BC)`

⇒ `tan 45^circ = h/x`

⇒ `1 = h/x`

⇒ `h = 50/sqrt(3)`

⇒ h = 28.87

Therefore, H = 50 – h

⇒ H = 50 – 28.87

⇒ H = 21.13

Hence, height pole is 21.13 m.