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 200 metres, what is the breadth of the river?

Answer 1

See the image attached:

Let AB be the width of the river

AC be the length of the bridge across the river i.e. 200m

The bridge AC makes and angle 45° with the river bank

∴ AC = 200 m and ∠CAB = 45°

In ΔBAC,

cos 45° = AB /AC

1/ √2 = AB / 200

AB = 200 / √2 = 100√2 m

Thus, the width of the river is  100√2 m

Answer 2

Hello Dear.

↔Refers to the attachment for the Question.↔

Let the Breadth of the River be x m.
∴ BC = x m.

Now,
 AC = 200 m.

We know, ΔABC is the Right angle Triangles.
∴ Applying Trigonometric Relations,

∵ Cos θ = AB/AC
∴ Cos 45° = AB/200
∴ 1/√2 = AB/200    [∵ Cos 45° = 1/√2
⇒ AB = 200 / √2
⇒ AB = 100√2   [∵ √2 = 1.414]
∴  AB = 141.4 m.

Hence the width of the river is 141.4 m. 

Hope it Helps.