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From a point P on the ground the angle of elevation of the top of a tower is 30° and that of the top of a flag staff fixed on the top of the tower, is 60°. If the length of the flag staff is 5 m, find the height of the tower. - Mathematics

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From a point P on the ground the angle of elevation of the top of a tower is 30° and that of the top of a flag staff fixed on the top of the tower, is 60°. If the length of the flag staff is 5 m, find the height of the tower.

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Solution

Let RQ be the tower and SR be the flag staff.

In PQR,

`tan30^@=(RQ)/(PQ)`

`=>1/sqrt3=h/x`

`=>x=hsqrt3 " .....(i)"`

In PQS

`tan 60^@=(SQ)/(PQ)`

`=>sqrt3=(h+5)/x`

`=>xsqrt()3=h+5" .....(ii)"`

From (i) and (ii), we get 

3h=h+5

2h=5

h=2.5 m

Hence, the height of the tower is 2.5 metres.

Concept: Heights and Distances
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