chapter-header

ML Aggarwal Solutions Class 10 Mathematics Solutions for Heights and Distances Exercise 20 in Chapter 20 - Heights and Distances

Question 12 Heights and Distances Exercise 20

A bridge across a river makes an angle of 450 with the river bank. If the length of the bridge across the river is 200 metres, what is the breadth of the river.

Question 12 Image - M L Aggarwal - Understanding ICSE Mathematics - Class 10 chapter Heights and Distances

Answer:

Solution:

In trigonometry, in particular, the angle of elevation is a frequently utilised notion in relation to height and distance. It can be characterised as an angle between the horizontal plane and an oblique line connecting the observer's eye to an object above his eye.

Consider AB as the width of river = x m

Length of bridge AC = 200 m

Angle with the river bank = 450

We know that

sin θ = AB/AC

Substituting the values

sin 450 = x/200

So we get

1/√2 = x/200

By cross multiplication

x = 200/√2

Multiplying and dividing by √2

x = 200/√2 × √2/√2

By further calculation

x = 200(1.414)/2

x = 100 (1.414)

x = 141.4 m

Hence, the breadth of the river is 141.4 m. M L Aggarwal - Understanding ICSE Mathematics - Class 10 chapter Heights and Distances Question 12 Solution image

Connect with us on social media!
2022 © Quality Tutorials Pvt Ltd All rights reserved