Question

The two palm trees are of equal heights and are standing opposite 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.​

Answer 1

the image help you solve the question

Answer 2

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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

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