Two buildings are collinear with the base of a tower and are at a distance 9m and 16m from the base of the tower. The angles of elevation from these two building of the top of the tower are complementary. What is the height of the tower?
Let the height of the tower be h And ∠CBD = θ and ∠ DAC = 90 – θ In ∆ BCD tan θ = CD/BC = h/9 …………(i) In ∆ ACD tan(90 - θ) = CD/AC cot θ = h/16 ……………………….(ii) On multiplying Equation (i) and (ii) tan θ × cot θ = h/9 × h/16 1 = h²/144 Now h = 12 m
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