2015 · Q64
The angles of elevation of the top of a tower from two points P and Q at distances m² and n² respectively, from the base and in the same straight line with it are complementary. The height of the tower is
Elementary MathematicsTrigonometry
- A(mn)¹/2}
- Bmn¹/2}
- Cm¹/2} n
- Dmn
Explanation
With tower height h, cotα = m²/h and cotβ = n²/h where α+β = 90°, so (m²/h)(n²/h) = cotα·cotβ = 1, giving h² = m²n² and h = mn (option D).