A bridge across a river makes an angle of 45⁰ with the river bank. If the length of the bridge across the river is 200 metres, what is the breadth of the river.

olution:

Consider AB as the width of river = x m

Length of bridge AC = 200 m

Angle with the river bank = 45⁰

We know that

sin θ = AB/AC

Substituting the values

sin 45⁰ = x/200

So we get

1/√2 = x/200

By cross multiplication

x = 200/√2

Multiplying and dividing by √2

x = 200/√2 × √2/√2

By further calculation

x = 200(1.414)/2

x = 100 (1.414)

x = 141.4 m

Hence, the breadth of the river is 141.4 m.

Hence Proved