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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=(RQPQ)
13=hx.....(i)
x=h3
In PQS,
tan60=SQPQ
3=h+5x.....(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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