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In order to cross a river, a person has to cover a distance of 250 m along the straight bridge from one end to the other. If the bridge makes an angle of $30 °$ with the edge of the river, what will be the width of the river?

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120m

125m

130m

135m

answer is B.

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Detailed Solution

Given that a person has to cover a distance of 250 m along the straight bridge from one end to the other and the bridge makes an angle of

30 °

with the edge of the river.
Constructing a diagram,
Question Image

Using the identity

sin θ = p e r p e n d i c u l a r Hypotenuse

Δ A B C

and substituting

θ

30 °

and AC=250 in the equation

sin θ = BC AC

⇒ sin 30 ° = BC 250 ⇒ B C = sin 30 ° 250 ⇒ B C = 12250 [∵ sin 30 ° = 12] ⇒ B C = 125 m

Thus the width of the river will be

125

m.
Therefore the correct option is 2.

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