Question

A bridge across a river makes an angle of 45degree with the river bank. If the lenght of the bridge across the river is 150m then the width of the river is .....................

Please help me out .

Answer 1

We can constructe a bridge like given in the figure. Since the bridge makes an angle of 45 degree it is given. Now by applying the formula we can get the answer. If u like comment

Answer 2

Length of the bridge = AC = 150cm

Let width of the river = AB = x metres, $\sf{\angle{ACB}=45°}$

From right ∆ABC,we have

$\longrightarrow$ $\sf{\sin(45)° = \frac{AB}{AC} }$

$\longrightarrow$ $\sf{ \frac{1}{ \sqrt{2} } = \frac{x}{150} }$

$\longrightarrow$ $\sf{x = \frac{150}{ \sqrt{2} } = \frac{150}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2}} }$

$\longrightarrow$ $\sf{75 \times 1.414}$

$\longrightarrow$ ${\boxed{\sf{106.05m}}}$

Hence, the width of the river is 106.05m.