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Question
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.
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.
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