2015 · Q44
A pole is standing erect on the ground which is horizontal. The tip of the pole is tied tight with a rope of length {12} m to a point on the ground. If the rope is making 30° with the horizontal, then the height of the pole is
Elementary MathematicsTrigonometry
- A2{3} m
- B3{2} m
- C3 m
- D{3} m
Explanation
This is a right-triangle trigonometry problem. The rope is the hypotenuse of length √12 m and makes 30° with the ground, so the pole's height is the side opposite 30°: height = √12 × sin 30° = √12/2 = √3 m. Option (a) 2√3 m is the trap from forgetting to halve (using the full rope length), and (c) 3 m comes from misreading √12 as 6. Hence option (d).