Question

A bridge across a river makes an angle
of 45° with the river bank. If the
length of the bridge across the
river is 150m, what is the width
of the liver ?
river​

Answer 1

Answer:

right triangle ABC, we have

sin45

∘

=

AC

BC

⇒

2

1

=

150

BC

⇒BC=

2

150

⇒BC=75

2

m

Hence, the width of the river is 75

2

m metres.

Answer 2

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.