Q21. Calculate the tangent length of a 5 degree curve, if the deflection angle is 60 degrees.
📚 Detailed Explanation: Tangent Length from Degree of Curve and Deflection Angle
This is another two-step problem in the same pattern as Q19: first convert the degree of curve to radius, then apply the tangent length formula — reinforcing the same multi-step workflow with a different final formula.
Step 1 — Convert degree of curve to radius (30 m chord convention):
R = 1719 / D = 1719 / 5 = 343.8 m
Step 2 — Apply the tangent length formula:
T = R tan(Δ/2)
T = 343.8 × tan(30°) = 343.8 × 0.5774 = 198.5 m ≈ 198.6 m
Why the Other Options Are Wrong
A — 172.5: Does not match the correct two-step calculation; possibly results from an incorrect trigonometric value or skipping the radius conversion step.
C — 360: Far too large for these inputs; may come from an arithmetic error such as using Δ directly (60°) instead of Δ/2 (30°) in the tangent function.
D — 596: Significantly overstates the tangent length; likely from a compounding error across both steps of the calculation.
Key Concepts for Students
- This question mirrors Q19’s structure exactly, but with the tangent formula instead of the apex distance formula: Both require converting degree of curve to radius first (R=1720/D, here rounded slightly differently as 1719/D), then applying a trigonometric curve-element formula using Δ/2.
- tan(30°) = 1/√3 ≈ 0.5774: Memorising standard trigonometric values for 30°, 45°, and 60° (sin, cos, tan) speeds up these calculations significantly, since these angles appear repeatedly throughout circular curve problems.
- Always halve Δ before applying tangent, chord, or apex distance formulas: Forgetting this halving step (as a hypothetical wrong path would do, using tan(60°) instead of tan(30°)) is the most common source of error across this entire family of curve-element formulas.