(Q15) A boat has to cross a river. It crosses the river by making an angle of 60o with the bank of the river due to the stream of the river and travels a distance of 600 m to reach the another side of the river. What is the width of the river?

Solution :

Let the width of the river = AB = x m

Angle made by the boat = °

Distance travelled = AC = m

From the figure

cos ° =
x
1
2
=
x
600
⇒ X =
600
2
= m.
ABCBankBank

A = Boat's place

C = Reach place of another side (or) Point of observation.

AC = Travelling distance of the boat ∠AC = 60o

AB = width of the river AB

In ∆ABC, sin° =
AB
AC
=
AB
AB = ×
=