A man sitting at a height of 20 m on a tall tree on a small island in the middle of a river observes...

Question

A man sitting at a height of 20 m on a tall tree on a small island in the middle of a river observes two poles directly opposite to each other on the two banks of the river and in line with foot of tree. If the angles of depression of the feet of the poles from a point at which the man is sitting on the tree on either side of the river are 60° and 30° respectively.

Find the width of the river.

Accepted Answer

Solution The term angle of depression refers to the angle produced between the horizontal line and the line of sight when an observer looks down at an object It calculates the variation in our field of vision as we glance down From the given data the fig is made Let width of river PQ x y m Height of tree AB 20 m So in ABP tan 60suposup AB BP 3 20 x x 20 3 m In ABQ tan 30suposup AB BQ 1 3 20 y y 203 So x y 20 3 203 20 203 3 803 Therefore the width of the river is 803 m

RD Sharma Solutions Class 10 Mathematics Solutions for Some Applications Of Trigonometry Exercise 12.1 in Chapter 12 - Some Applications Of Trigonometry