Q6 of 120 Page 99

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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