Q27 of 50 Page 1

The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45°. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60°, then find the height of the flagstaff. [Use √3 = 1.73]


Let BC and CD be the heights of the tower and the flagstaff respectively.


Given AB = 120m, ∠BAC = 45°, ∠BAD = 60°


Let CD = x


In Δ ABC,


⇒


⇒


⇒ BC = 120m


In Δ ABD,


⇒


⇒


⇒ BC + CD = 120√3


⇒ 120 + x = 120√3


⇒ x = 120√3 – 120


⇒ x = 120 (√3 – 1)


⇒ x = 120 (1.732 – 1)


⇒ x = 120 (0.732)


⇒ x = 87.84


∴ The height of the flagstaff is 8.78 m.


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