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Question
A flag-staff stands on 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 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flag-staff.
Solution
Let BC be the tower height of 5 m. flag height is hm and an angle of elevation of the top of the tower is 45° and an angle of elevation of the top of the flag is 60°.
Let AC = hm and BC = 5 m and ∠ADB = 60°, ∠CDB = 45°
We have the corresponding angle as follows
So we use trigonometric ratios.
In a triangle ΔBCD
`=> tan 44^@ = (BC)/(BD)`
`=> 1 = 5/x`
`=> x= 5`
Again in a triangle ABD
`=> tan 60^@ = (AB)/(BD)`
`=> sqrt3 = (5 + h)/5`
`=> h = 5(sqrt3 - 1)`
`=> h = 3.66`
Hence the height of flag is 3.66 m
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