Question

An aeroplane at an altitude of 200 m observes the angles of depression of opposite points on the two banks of a river to be 45° and 60°. Find the width of the river.

Answer 1

Let AD be the height of the aeroplane and BC = x m be the width of the aeroplane. 

Given: AD = 200 m 

In ΔABD

`"AD"/"BD" = tan45^circ`

⇒ `"AD"/"BD" = 1`

⇒ AD = BD

⇒ BD = 200 m   ...(∵ AD = 200 m)

Now, 

In ΔACD

`"AC"/"CD" = tan 60^circ`

⇒ `"AC"/"CD" = sqrt(3)`

⇒ `"CD" = "AC"/sqrt(3)`

⇒ `"CD" = 200/sqrt(3)`

⇒ BC = BD + CD 

⇒ BC = `200 + 200/sqrt(3)`

⇒ BC = 200 + 115.47

⇒ `"BC" = 315.4` m

Thus, the width of the river is 315.4 m.