Question

Two ships are approaching a light house from opposite directions.The angle of depression of the two ships from the top of the light house are 30 and 45 degrees.If the distance between the two ships is 100 metres, find the height of the light house.

Answer 1

heyaa friend!!!

let the height of light house be 'h'
distance between the ships = 100
let distance between ship 1 to tower be 'x'
therefore distance between ship 2 to tower = 100-x

tan 30 = h/x
1/√3 = h/x
x = √3h............ 1

tan 45 = h/100 - x
1 = h/100 - x
h = 100 - x............ 2
by eq 1 and 2
h = 100 - h √3
h + h√3 = 100
h(1 + √3 ) = 100
h = 100/1 + √3
h = 100* 1 - √3 / 1 + √3 * 1 - √3
h= 100 - 100√3 / 2
h = 50 - 50√3

hope thiss helps u:)