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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.

Answer:

**Solution:**

In trigonometry, in particular, the angle of elevation is a frequently utilised notion in relation to height and distance. It can be characterised as an angle between the horizontal plane and an oblique line connecting the observer's eye to an object above his eye.

Consider AB as the width of river = x m

Length of bridge AC = 200 m

Angle with the river bank = 45^{0}

We know that

sin θ = AB/AC

Substituting the values

sin 45^{0} = 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.**

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