Question

In the shape of a straight path across a river makes an angle of 60° with the width of the river if the length of the bridge is 100 M find the width of the river

Answer 1

Let AB be the width of the river and AC be the bridge.

In the triangle ABC,

Cos 60 = AB / AC

1 / 2 = AB / 100 => AB = 50m

Hence the width of the river is 50 m.

Answer 2

Given:

A bridge in the shape of a  straight path across a river makes an angle of 60° with the width of the river

The length of the bridge = 100 m

To Find:

The width of the river

Solution:

The width of the river is 50m.

In the diagram attached below, AB represents the bridge that makes an angle of 60° with the width BC of the river.

Since ΔABC is a right-angled triangle with ∠C = 90°,

We can apply trigonometry to find an unknown side.

cos Ф = Base / Hypotenuse

For the given figure,

cos 60° = BC / AB

Substituting cos 60° = 1/2 and AB = 100m,

1/2 = BC / 100

or BC = 100/2

= 50m