**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,

AB^{2 }= OA^{2}+OB^{2}

d^{2 }= h^{2}cot^{2} α + h^{2} cot^{2}β

h = d/√cot^{2}a + cot^{2}β [using (i) and (ii)].