Question

A person, standing on the bank of a river,
observes that the angle subtended by a tree on
the opposite bank is 60°. When he retreats 20 m
from the bank, he finds the angle to be 30°. Find
the height of the tree and breadth of the river.​

Answer 1

Answer:

Breadth of the river = 10 meter

Height of the tree = 10√3

Step-by-step explanation:

Solution:

A person standing on bank sees the branch of the tree of the opposite to be 60 degree

If the person retreats 20m back he then face the branch at 30 degree as we can see in the diagram attached.

Height of branch from ground = h

Let x be the length of river at which tree forms 60 degree.

To find: Height and breadth of the branch and river.

Tan 60 = h/x

If the person backs 20 m it becomes = Tan 30° = h/x+20

Tan 60° = √3

Tan 30°= 1/√3

Substituting the values we get

√3= 1/x

1/√3 = h/x+20

h=√3x

x+20 = √3h

Substituting the value of h in x+20=√3h

h+20= √3√3x

3x = x + 20

2x = 20

x = 10

h= 10√3

HOPE THIS HELPS YOU

PLEASE MARK AS BRAINIEST