2024 · Q53
The angles of elevation of the top of a tower from two points A and B at a distance of x m and (x + 5) m from the base of the tower of height 6 m and in the same straight line with it are complementary. What is the value of x?
Elementary MathematicsTrigonometry
- A4 m
- B5 m
- C6 m
- D9 m
Explanation
Complementary elevation angles give (6/x)(6/(x+5)) = 1, i.e. x² + 5x − 36 = 0. Factoring gives (x + 9)(x − 4) = 0, so x = 4 m, option (a).