The angle of elevation of the top of a tower from a point A due south of the tower is a and from … that the height of the tower is…
Let OP be the tower and let A and B be two points due south and east respectively of the
tower such that ∠OAP = α and ∠OBP = β. Let OP = h.
In △OAP, we have
tan α = h/OA
OA = h cot α ……..(i)
In △OBP, we have
tan β = h/OB
OB = h cot β ……..(ii)
Since OAB is a right angled triangle. Therefore,
AB2 = OA2+OB2
d2 = h2cot2 α + h2 cot2β
h = d/√cot2a + cot2β [using (i) and (ii)].