Question

A person, standing on the bank of a river.
observes that the angle subtended by a tree on the
opposite bank is 60" When he retreats 20 m from
the bank, he finds the angle to be 30. Find the
height of the tree and breadth of the river.
(3-1.732)​

Answer 1

Answer:

h = 10√3 m and breadth of river = 10 m.

Step-by-step explanation:

See the attached figure:

Tan60 = h/x

=>  √3 = h/x

=> h = x√3.  ---------  [1]

Tan30 = h/(x + 20)

=> 1/√3 =  h/(x + 20)

=> x + 20 = h√3.

Substitute value of h from [1],

=> x + 20 = 3x

=> 2x = 20

=> x = 10 m.

=> h = 10√3.