a bridge across a river makes an angle of 45⁰ with the river bank.if the length of the bridge across the river is 150 m, then the width of the river is:

ans 150(underroot)3

Question

a bridge across a river makes an angle of 450 with
the river bank if the length of the bridge across the river is 150
m, then the width of the river is:
ans 150(underroot)3

Gursheen kaur. · Accepted Answer

Let AB be the width of the river and

AC be the length of the bridge across the river.

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

∴ AC = 150 m and ∠CAB = 45°.

In ΔBAC,

$\Rightarrow \cos 45 ° = \frac{AB}{AC} [∵ \cos θ = \frac{Base}{Hypotenuse}] \Rightarrow \frac{1}{\sqrt{2}} = \frac{AB}{150 m} \Rightarrow AB = \frac{150 m}{\sqrt{2}} = \frac{150 \sqrt{2}}{2} m = 75 \sqrt{2} m$

Thus, the width of the river = $75 \sqrt{2} m$ .

2

a bridge across a river makes an angle of 450 with the river bank.if the length of the bridge across the river is 150 m, then the width of the river is: ans 150(underroot)3

a bridge across a river makes an angle of 45⁰ with the river bank.if the length of the bridge across the river is 150 m, then the width of the river is:

ans 150(underroot)3