when viewed from a point P, due north of a tall building, the angle of elevation of the top of the building is 40 degree ; when viewed from a point Q due east of the building, the angle of elevation is 35 degree. If the distance PQ is 120m, find the height of the building.

Answer 1

Let's set up some labels.
T = top of building
B = bottom of building
y = BP
x = BQ
If the building has height h, then

h/x = tan 40°
h/y = tan 35°
so, x tan 40° = y tan 35°
x^2+y^2 = 120^2

solving that, we get
x = 76.88
y = 92.13
h = 64.5

Answer 2

steve you are perfectly crrct. Thank you sir