Question

A palm tree stands on the bank of a river. A post is fixed in the earth on the other bank just opposite to the palm tree. On moving \frac{7}{3} metres from the post along the bank, it is found that the tree makes an angle of 60° at that point with respect to this bank. Find the width of the river.
Please show me the diagram too.​

Answer 1

Answer:

Let the height of the tree = h and the width of the river =w

The angle of elevation when standing on the bank = 60

∘

When moved 40 m away from the bank, angle of elevation = 30

∘

Now, tan∠ of elevation =

distance

height

Now, tan60=

w

h

3

=

w

h

h=w

3

(1)

Also, tan30=

w+40

h

3

1

=

w+40

h

h=

3

w+40

(2)

From (1) and (2)

w

3

=

3

w+40

3w=w+40

w=20 m

The width of the river is 20 m.

solution