Question

The angles of elevation and depression of the top and bottom of a light house from the top of a 60m high building are 30o and 60o respectively. Find-; 1) the difference between the heights of the light house and the building; 2) the distance between the light house and the building

Answer 1

heyyaa friend!!

let the height of light house be ' h'
let the distance between them be 'x'

tan 30 = h - 60 / x
1/√3 = h - 60 / x
x = √3(h - 60 )
x = √3h - 60√3.............1
tan 60 = h/x
√3 = h/x
x = h/√3......2
by eq 1 and 2
√3h - 60√3 = h/ √3
√3h - h/√3 = 60√3
3h - h /√3 = 60√3
2h/√3 = 60√3
2h = 60√3*√3
2h = 180
h = 90m
1) difference between the heights = 90 - 60 = 30m
2) distance between them = x = h/√3 = 90√3
90√3 / √3* √3 = 90√3 / 3 = 30√3 m

hope this helpss if it does plzz mark it as brainliest :):)