Question

The two palm tree are equal height are standing opposite each other on either side of the river which is 80 metre wide from a point between them on river the angle of elevation of the top of the trees are 60 degree and 30 degree respectively find the height of the trees and the distance of the point O from the tree​

Answer 1

Consider the above figure

tan60

0

=

80−x

b

⇒

3

=

80−x

b

⇒b=

3

x−80

3

....(i)

and,

tan30

0

=

3

1

=

x

a

x=a

3

...(ii)

b=3a−80

3

Or

3a−b=80

3

Now it is given that the heights are equal.

Hence

a=b=h

Therefore

2h=80

3

h=20

3

=2(17.32)

=34.64m

Hence

x=h

3

=20(3)=60m

solution