Question

two pillars of equal height stand on either side of a roadway which is 150m wide. from a point on the roadway between the pillars the angle of elevation of the top of the pillars are 60°and 30°. find the height of the pillars and the position of the point

Answer 1

let x be the position of point from first pillar.
let h be the height of the pillar. 

First draw a rough diagram.
use trigonometry and you will see that

h/(x+150)=tan 30=1/(3)^1/2
h/x=tan 60=3^1/2

after solving,

x*(3)^1/2=(150+x)/(3)^1/2
3x=150+x
2x=150
x=75
h=75*(3)^1/2

Answer 2

answer is this

x=37.5 m

x and 150-x are the two distances