2020 · Q57
The angles of elevation of the top of a tower from two points at distances p and q from the base and on the same straight line are 27° and 63° respectively. What is the height of the tower?
Elementary MathematicsTrigonometry
- Apq
- B√pq
- Cpq/2
- D√pq/2
Explanation
From the two right triangles, tan27° = h/p and tan63° = h/q. Since tan63° = cot27° = 1/tan27°, multiplying gives h²/(pq) = 1, i.e. h = √pq.