A bridge across a river makes an angle of 45Âş with the river bank(fig.).Â If the length of the bridge across the river is 150 m, what is thewidth of the river?

Question

A bridge across a river makes an angle of 45Âş with the river bank(fig.).Â If the length of the bridge across the river is 150 m, what is thewidth of the river?

Philoid · Accepted Answer

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Given:

Length of the bridge, AC = 150 m

Angle of elevation, θ = 45°

To find: Width of the bridge, AB

Solution:

In right angled Δ ABC,

sin θ = [Opposite] / [Hypotenuse]

sin 45° = AC/AB

And also the opposite side is AB and the hypotenuse side is AC

sin 45° = AB/AC

AB = AC sin 45 ^º

= 150 × (1 / √2)

= 150 × 1.414

= 106.066 m

Therefore the width of the river is 106.07 m.