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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 the width of the river CD be x,
In ΔABC,
tan 60° = `"AB"/"BC"`
√3 = `250/"BC"`
BC = `250/sqrt3 xx sqrt3/sqrt3`
BC = `(250/3)sqrt3` .....(i)
In Δ ABD,
tan 45° = `"AB"/"BD"`
⇒ AB = BD = 250 ....(ii)
∴ BD = BC + CD
∴ 250 = `(250/3) sqrt3 + x` ....(using (i) and (ii))
∴ x = 250 - `(250/3) xx 1.732`
∴ x = 250 - 83.33 x 1.732
∴ x = 250 - 144.33
∴ x = 105.67 m
∴ x = 106 m .....(to the nearest whole numbers)
Thus, width of the river is 106 m.
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