7(i)
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.
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In △APB,
⇒ tan 42° = $\frac{AB}{AP}$
⇒ 0.9004 = $\frac{AB}{100}$
⇒ AB = 0.9004 × 100 = 90.04 m
In △APF,
⇒ tan 54° = $\frac{AF}{AP}$
⇒ 1.3764 = $\frac{AF}{100}$
⇒ AF = 1.3764 × 100 = 137.64 m
From figure,
BF = AF - AB = 137.64 - 90.04 = 47.60 ≈ 48 m.
Hence, height of flagstaff = 48 m.