Question

From a point on a ground the angle of elevation from a tower is observed to be 60 degree. From a point on 40meter vertically above the first point of observation the angle of elevation from a tower is 30degree. Find the height of the tower and horizontal distance from the point of observation

Answer 1

My diagram:
A vertical line PQ, to show the tower, P at ground-level
Another vertical AB, the points of observation with A at ground-level
let AP = x
draw a horizontal from B to meet PQ at R

in triangle APQ
tan 60 = (h+40)/x
x = (h+40)/tan60

in triangle BRQ
tan30 = h/x
x = h/tan30 ***

(h+40)/tan60 = h/tan30
htan60 = htan30 + 40tan30
h(tan60 - tan30) = 40tan30
h = 40tan30/(tan60-tan3)
= ...

you do the button-pushing,
Once you have h, sub that back into ***
to get x