Question

from the top and foot of a tower 40m high the angle of elevation of the top of a light house is found to be 30degree and 60 degree find the height of the light house also find its distance of the top of the light house from the foot of the tower

Answer 1

Angle of elevation from the top of tower to the top of light house is 30° and from bottom is 60°
Now let the distance between the foots of lighthouse and tower be X and the height of tower be H
Now,
tan30°=(H-40)/X
=> H√3 - 40√3=X
Let this be equation 1.
Also, tan60°=H/X
=> H=X√3
Let this be equation 2.
Now on solving these 2 equations, we get that
H=60
& X=20√3
Now the distance of the top of lighthouse and foot of tower is √(X²+H²)
= 40√3