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Question
A vertical tower standing on a horizontal plane is surmounted by a vertical flagstaff. At a point 100 m away from the foot of the tower, the angle of elevation of the top and bottom of the flagstaff are 54° and 42° respectively. Find the height of the flagstaff. Give your answer correct to nearest metre.
Solution
In ΔPAB,
`(AB)/(PA) = tan 42^circ`
`(AB)/100 = 0.9004`
`\implies` AB = 90.04 m
In ΔPAF,
`(AF)/(PA) = tan 54^circ`
`(AF)/100 = 1.3764`
`\implies` AF = 137.64 m
FB = 137.64 m – 90.04 m
= 47.60 m
= 48 m
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