Question

There is a small island in a river 18 m wide, and there is a tree

on the island. Two men are standing at the opposite banks of the

river facing the tree. They observe the angles of elevation as 60º

and 30º respectively. What is the height of the tree? with diagram​

Answer 1

Given : There is a small island in a river 18 m wide,

a tree  on the island.

Two men are standing at the opposite banks of the  river facing the tree

They observe the angles of elevation as 60º  and 30º respectively

To Find : What is the height of the tree

Solution:

Distance of tree from one end = a

distance from other end = b

width of island = 18 m

=> a + b = 18 m

Height of tree = h m

Tan 60°  = h/a

=>√3 = h/a

=> a  = h/√3

Tan 30°  = h/b

=>1/√3 = h/b

=> b = h√3

a + b = 18

 h/√3 + h√3 = 18

=> h + 3h = 18√3

=> 4h = 18√3

=> 2h = 9√3

=> h  = 9√3 / 2

height of the tree  = 9√3 / 2 m

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