A flagpole is erected at the top of a building. The angle of elevation of the top and foot of the flagpole from a point 100 m away, on the same level as that of the foot of the building, are 33° and 31° respectively. Find the height of the flagpole. Give your answer correct to the nearest metre.
Let height of building (BC) = h m and height of flagpole (CD) = x m.
tan 31° = \frac{\mathrm{h}}{100}
h = 100 tan 31° = 60.09 m
tan 33° = \frac{\mathrm{h}+\mathrm{x}}{100}
h + x = 100 tan 33° = 64.94 m
x = 64.94 − 60.09
= 4.85 m
≈ 5 m
Therefore, the height of the flagpole is 5 m.
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