Answer :

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 ΔOAP, we have

tan α = h / OA

OA = h cot α ……………. (i)

In ΔOBP, 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 = [Using (i) and (ii)].

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