Two boats approach a light house in mid-sea from opposite directions. The angles of elevation of the top of the light house from two boats are 30° and 45° respectively. If the distance between two boats is 100 m, find the height of the light house.
In the fig AB is the light house of height h (m)
In ∆ABC
tan 30° = 
= 
x = 100 - √3 h ……………(1)
In ∆ABD
tan 45° = 
1= 
x = h …………(2)
On substituting value of x from eqn (2) in eqn (1)
h = 100 - √3 h
h + √3 h = 100
h (1 + √3) = 100
h = 
= 
⇒ 50 (√3 - 1)
Therefore height of the light house is 50 (√3 - 1)m
60