Question

A vertical tower of height 20 m stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane, the angle of elevation of the bottom and top of the flagstaff are 45 degree and 60 degree respectively find the value of h.


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Answer 1

Answer:

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Answer 2

14.64 m is height of the flagpole.

Let A be the bottom of flagpole and B be the top of the flagpole. Let O be the bottom of the tower and C be the elevation point of observation.

∴ In ΔCOA,

OA = 20 m = Height of tower

and ∠ACO = 45°.

∴ tan 45° = OA/OC

∴ OC = 20 / tan 45°

∴ OC = 20 m

In ΔOBC,

OB = 20+h

and ∠BCO = 60°

∴ tan 60° = OB/OC

∴ 20 + h = tan60° × 20

∴ h = 20 × (√3 - 1)

∴ h = 14.64 m