Angle Of Elevation Of Top Of Tower From Point Due South Of Tower And From Due East Of Tower Is

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…

Answers:

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)].