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Question
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.
Solution
Let A be the position of the aeroplane and let BC be the river. Let D be the point in BC just below the aeroplane.
For ΔADC,
`tan 45^@ = h/y`
`=> 1 = 250/y`
`=> y = 250 m`
For ΔADB
`tan 60^@ = (AD)/(DB)`
`=> sqrt3 = h/x`
`=> sqrt3 = 250/x`
`=> x = 250/sqrt3 m`
Thus the width of the river = `DB + DC = 250 + 250/sqrt3 = 394 m`
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