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 retreated 20m from the bank, he finds the angle to be 30°. Find the height of the
tree and the breadth of the river

Answer 1

Answer:

Let AB be the breadth of the river and BC be the height of the tree which makes a ∠ of 60

∘

at a point A on the opposite bank.

Let D be the position of the person after retreating 20 m from the bank.

Let AB =x metres and BC =h metres.

We know, tan(θ) = Opposite / Adjacent

From right ∠ed △ ABC and DBC,

we have tan60

∘

=

AB

BC

and tan30

∘

=

20+x

h

⇒

3

=

x

h

and

3

1

=

x+20

h

⇒h=x

3

and h=

3

x+20

⇒x

3

=

3

x+20

⇒3x=x+20⇒x=10m

Putting x=10 in h=

3

x, we get

h=10

3

=17.32m

Hence, the height of the tree =17.32 m and the breadth of the river =10 m.

Answer 2

Answer:

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 retreated 20m from the bank, he finds the angle to be 30°. Find the height of the

tree and the breadth of the river