Chapter 13 - Height and Distance

Example 2. A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60⁰. When he moves 40m away from the bank, he finds the angle of elevation to be 30⁰. Find the height of the tree and the width of the river.

Solution:- Let height of the tree be y and width of the river be x. CD = 40m

In

tan 30⁰ = AB/BD

In

tan 60⁰ =AB/BC

Putting value of y from (ii) to (i)

Height of the tree =

Width of the river = 20m.