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^circ = h/y`

⇒ `1 = 250/y`

⇒ y = 250 m

For ΔADB

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

⇒ `sqrt(3) = h/x`

⇒ `sqrt(3) = 250/x`

⇒ `x = 250/sqrt(3) m`

Thus, the width of the river = DB + DC 

= `250 + 250/sqrt(3)` 

= 394 m