A flag-staff stands at the top of a 5 m high tower. From a point on the ground,the angle of elevation of the top of the flag-staff is 60º and from the samepoint, the angle of elevation of the top of the tower is 45º. Find the heightof the flag-staff.

Question

Philoid · Accepted Answer

Given:

Height of the tower, h = 5 m

Angle of elevation of the top of the flag staff, θ = 60°

Angle of elevation of top of tower, ϕ = 45 °

To find: Height of the flag staff.

Solution:

Let BC be the height of the tower and DC be the height of the flag-staff.

In right angled Δ ABC,

AB = BC cot 45°

AB = 5 m ………………….(i)

In right angled Δ ABD,

AB = BD cot 60°

AB = (BC + CD) cot 60°

AB = (5 + CD) × ( 1 / √ 3) ………………….(ii)

Equating (i) and (ii)

(5 + CD) × (1 / √ 3) = 5

(5 + CD) = 5 × (√ 3)

CD = (5× √ 3 ) - 5

= 5(1.732 - 1)

= 5 × 0.732

= 3.66 m

Therefore the height of the flag-staff is 3.66 m