2025 · Q66
Two poles of heights 10 m and 15 m are 25 m apart. What is the height of the point of intersection of the lines joining the tip of each pole to the foot of the other?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A4.8 m
- B5 m
- C6 m
- D6.4 m
Explanation
By similar triangles, the crossing height h satisfies 1/h = 1/10 + 1/15. Solving gives h = 150/25 = 6 m, equivalently h = h1*h2/(h1+h2). Measuring from the wrong pole, or averaging the two heights instead, is the classic mix-up.