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

Answer:

Let AB and CD aree two trees on two sides of the river

Let their height be h and the distance of the point O from tree AB be x

Consider triangle AOB

tan60 =h/x=√3. This gives h=x√3

Consider triangle DOC

tan30=h/(80-x)= 1/√3. This gives

h√3= 80-x

Put h=x√3 in this equation

x√3×√3 =80-x

3x+x= 80

4x =80

x= 20

h=20√3