The angle of elevation of the top of an unfinished tower at a point distant 78 m from its base is 30°. How much higher must the tower be raised (in m) so that the angle of elevation of the top of the finished tower at the same point will be 60º?

Question

Question

This question was previously asked in

SSC CGL 2021 Tier-I (Held On : 11 April 2022 Shift 1)

Answer 1

Given:

The angle of elevation of the top of an unfinished tower at a point = 30°

The angle of elevation of the top of the finished tower at the point = 60°

The distance from the tower to the point = 78 m

Calculation:

F4 Madhuri SSC 06.06.2022 D4

Here, OC = Height of the unfinished tower

AC = The height will be the finished tower's height

In ΔOBC, tan 30° = OC/BC

⇒ 1/√3 = OC/78 [∵ tan 30° = 1/√3]

⇒ OC = 78/√3

⇒ OC = (78 × √3)/(√3 × √3) = 26√3 .....(1)

Let, the height of the tower will be raised (AO) = x

In ΔABC, tan 60° = AC/BC

⇒ √3 = (OC + x)/78 [∵ tan 60° = √3]

⇒ x + OC = 78√3

⇒ x + 26√3 = 78√3

⇒ x = 78√3 - 26√3 = 52√3

∴ The tower will be raised (in m) 52√3 meters

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