Question

34. The two palm trees are of equal heights and are
standing opposite to each other on either side
of the river, which is 80 m wide. From a point o
between them on the river the angles of elevation
of the top of the trees are 60° and 30°, respectively.
Find the height of the trees and the distances of
the point O from the trees.
(5)​

Answer 1

Answer:

Let Palm tree be poles

tan600=80−xb

⇒3=80−xb

⇒b=3x−803 ....(i)

and,

tan300=31=xa

x=a3 ...(ii)

b=3a−803

Or

3a−b=803

Now it is given that the heights are equal.

Hence

a=b=h

Therefore

2h=803

h=203

=2(17.32)

=34.64m

Hence

x=h3

=20(3)=60m