Mathematics
An aeroplane at an altitude of 250 m observes the angle of depression of two boats on the opposite banks of a river to be 45° and 60° respectively. Find the width of the river. Write the answer correct to the nearest whole number.
Heights & Distances
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Answer
Let aeroplane be at point D and boats be at point A and B. Since, aeroplane is at an altitude of 250 m therefore,
∴ CD = 250 m.
From figure,
∠DAC = ∠XDA = 45° (Alternate angles are equal)
∠DBC = ∠YDB = 60° (Alternate angles are equal)
Considering right angled △BCD, we get
Considering right angled △ACD, we get
Width of the river (AB) = AC + BC = 144.34 + 250 = 394.34 meters.
Rounding off to nearest meter AB = 394 meters.
Hence, the width of the river is 394 meters.
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