let height of lighthouse be y
let the distance of the first ship from the base of the light house be x
thus the distance of the second ship from the base of the light house is 100 - x
angle of depression to first ship is 45 thus
tan (45) = y/x # height of light house/distance of ship from base of lighthouse
thus y/x = 1
thus x = y
angle of depression to second ship is 30 thus
tan(30) = y/(100-x)
1/sqrt(3) = y/(100-y)
y*sqrt(3) = 100 -y
100 = y*sqrt(3) + y = y*(1.732 + 1) = y*2.732
y = 100/2.732 = 36.60m
