Let
h = height of building
x = distance of observer from the building
Then, assuming that the antenna is not set back from the edge of the building, we have
1: h/x = tan45°
2: (h+12)/x = tan60°
From (1), h=x, so in (2),
(h+12)/h = √3
Now just find h.
A 12m tall antenna sits on top of a building. A person is standing some distance away from the building. If the angle of elevation between the person and the top of the antenna is 60°, and the angle of elevation between the person and the top of the building is 45°, how tall is the building and how far away is the person standing?
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