Question

एक नदी के ऊपर एक पुल नदी तट के साथ 45 डिग्री का कोण बनाता है नदी के ऊपर पुल की लंबाई ढाई सौ मीटर है तो नदी की चौड़ाई क्या होगी​

Answer 1

Given:

A bridge across a river makes an angle of 45°  with the riverbank

If the length of the bridge across the river is 250 m

To find:

What is the width of the river?

Solution:

To solve the given problem we will use the following trigonometric ratios of a triangle:

$\boxed{\bold{sin\:\theta = \frac{Perpendicular}{Hypotenuse} }}$

Referring to the figure let's assume the following:

"AC" → the length of the bridge across the river = 250 m

"BC" → width of the river

"∠CAB" → the bridge makes an angle with the bank of the river = 45°

Here we have,

BC = perpendicular

AC = hypotenuse

θ = 45°

∴ $sin\:\45 = \frac{BC}{AC}$

$\implies \frac{1}{\sqrt{2} } = \frac{BC}{250}$

$\implies BC = \frac{250}{\sqrt{2} }$

on multiplying and dividing by √2

$\implies BC = \frac{250}{\sqrt{2} } \times \frac{\sqrt{2} }{\sqrt{2} }$

$\implies BC = \frac{250}{2 } \times \sqrt{2}$

$\implies \bold{BC = 125 \sqrt{2}}$

Thus, the width of the river is → $\underline{\bold{ 125 \sqrt{2}}}$.

------------------------------------------------------------------------------------------------

Also View:

From a point on a bridge across the river, the angles of depression of the banks on opposite sides of the river are 30° and 45°, respectively. If the bridge is at a height of 3m, Find the width of the river.

https://brainly.in/question/1748093

A person observes two banks of a river at angles of depression theta 1 and theta 2(theta 1<theta 2) from the top of a tree of height h which is at a side of the river. The width of the rivers is d. Draw the diagram for a given situation.​

https://brainly.in/question/9095669

A bridge across a river makes an angle of 45°with the river bank if the length of the bridge across the river is 200m find the width of the river

https://brainly.in/question/2443127

our palm tree stands on the bank of the river. a post is fixed in the Earth on the other bank just opposite to the Palm tree. on moving 7 roots 3 metres from the post along the bank, it is found that the tree makes an angle of 60 degrees at that point with respect to this Bank. let's find the width of the river​

https://brainly.in/question/12242884