Answer :

Given:

Height of the flagstaff, h = 7 m

Angle of elevation of the bottom of flagstaff, θ = 30°

Angle of elevation of top of flag staff, ϕ = 45 °

To find: Height of the tower

Solution:

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

In right angle Δ ABC,

AB = BC cot 30°

AB = BC × √ 3 …………………. (i)

In right angled Δ ABD,

AB = BD cot 45°

AB = (BC + CD) cot 45°

AB = (BC + 7) …………………. (ii)

Equating (i) and (ii)

(BC + 7) = BC × √3

BC( √3 - 1) = 7

BC = 7/0.73

= 9.58 m

Therefore the height of the tower is 9.58 m.

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