2019 · Q34
The angles of elevation of the tops of two pillars of heights h and 2h from a point P on the line joining the feet of the two pillars are complementary. If the distances of the feet of the pillars from the point P are x and y respectively, then which one of the following is correct?
Elementary MathematicsTrigonometry
- A2h² = x²y
- B2h² = xy²
- C2h² = xy
- D2h² = x²y²
Explanation
tan of the first elevation = h/x, tan of the second = 2h/y. Complementary angles have tan A = cot B, so h/x = y/(2h), giving 2h^2 = xy.