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.

Answer 1

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`