[Directions: The chainage of the intersection point of two straights is 1060 m, and the angle of intersection is 120°. If radius of a circular curve to be set out is 570 m, and peg interval is 30 m.] What is the length of the curve?
- A190 π mCorrect
- B185 π m
- C180 π m
- D170 π m
Solution
Concept
Curve length = R × deflection angle (in radians). Deflection angle Δ = 180° − angle of intersection.
Formula
Δ = 180° − I; L = πRΔ/180
Step-by-step solution
1. Angle of intersection I = 120°. 2. Deflection angle Δ = 180° − 120° = 60°. 3. L = πRΔ/180 = π × 570 × 60/180. 4. L = 570π/3 = 190π m (about 596.9 m).
Explanation
The curve turns through the deflection angle, not the angle of intersection. Here Δ = 60°, so the curve length is one-sixth of a full circle of radius 570 m. This gives 190π m.
Why the other options are wrong
B (185π), C (180π) and D (170π) come from wrong angle or arithmetic. Using 120° directly gives 380π, which is not an option.
Shortcut
Δ = 60° means L = πR/3 = 570π/3 = 190π.
Common mistake
Using the angle of intersection (120°) in place of the deflection angle (60°).
Correct answer: A) 190 π m