The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is .


Let BC = s; PC = t

Let height of the tower be AB = h.


ABC = θ and APC = 90° - θ


( the angle of elevation of the top of the tower from two points P and B are complementary)



In


In



Multiplying eq. 1 and eq. 2, we get




h2 = st


h = st


Hence the height of the tower is √st.


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