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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]

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#### Solution

Solution:

Let AB is the tower of height h meter and AC is flagstaff of height x meter.

∠APB=45° and ∠BPC =60°

`Tan 60 = (x+h)/120`

`sqrt3=(x+h)/120`

`x=120sqrt3-h`

`tan 45=h/120`

therefore height of the flagstaff =

`=120sqrt3-120`

`=120(sqrt3-1)`

`=120 xx73`

`=87.6 cm`

Concept: Heights and Distances

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