Question

An aeroplane, at an altitude of 250 m, observes the angles of depression of two boats on the opposite banks of a river to be 45° and 60° respectively. If the boats are on the opposite sides of the aeroplane, find the width of the river. Write the answer correct to the nearest whole number.

Answer 1

Let A be the position of the airplane and let BC be the river. Let D be the point in BC just below the airplane.

B and C be two boats on the opposite banks of the river with angles of depression 60° and 45° from A. 

In ΔADC, 

`tan 45^circ = (AD)/(DC)`

`=> 1 = 250/y`

`=>` y = 250 m = DC

In ΔADB,

`tan 60^circ = (AD)/(BD)`

`=> sqrt(3) = 250/x`

`=> x = 250/sqrt(3)`

= `(250sqrt(3))/3`

= `(250 xx 1.732)/3`

= 144.3 m = BD

∴ BC = BD + DC

= 144.3 + 250

= 394.3 ≈ 394 m

Thus, the width of the river is 394 m.