The length of the first sub chord is 10 m and the radius of the curve is 200 m. Find the first tangential angle for setting out a circular curve.

Detailed Explanation: Tangential Angle for the First Sub-Chord

The tangential (deflection) angle method of curve setting requires computing a small angle for each chord along the curve, starting with the first (often shorter) sub-chord. This question tests the standard formula and, critically, correct conversion of the result into degrees-minutes-seconds.

Solution:
The tangential angle δ (in minutes of arc) for a chord of length c on a curve of radius R is given by the standard field formula:

δ (in minutes) = 1718.9 × c / R

Given c = 10 m, R = 200 m:
δ = 1718.9 × 10 / 200 = 17189/200 = 85.945 minutes

Converting to degrees-minutes-seconds:
85.945' = 1° 25.945' = 1° 25' + (0.945 × 60)" = 1° 25' 56.7" ≈ 1° 25' 57"

Why the Other Options Are Wrong

B — 100°: This is wildly too large for a tangential angle on a gentle, large-radius curve — tangential angles for individual short chords are always small (a few degrees at most), since they represent only a fraction of the total curve's deflection.

C — 85.95°: This is the numerically correct intermediate value (85.945) but with the WRONG UNIT — the formula's result of 85.945 is in minutes of arc, not degrees. Treating it as degrees gives an answer roughly 60 times too large.

D — 100: This unitless value does not correspond to any correctly computed quantity in this problem.

Key Concepts for Students

• The 1718.9 formula gives MINUTES, not degrees — the single most common trap in this topic: Always remember to convert the raw formula output from minutes into degrees-minutes-seconds before reporting a final answer; treating the raw number as degrees (as in incorrect option C) is the classic error this question is designed to catch.
• Converting decimal minutes to minutes-seconds: Once you have X.YYY minutes, the whole number part is minutes, and the decimal part × 60 gives seconds. Here, 85.945' → 85' + 0.945×60" = 85' 56.7", and since 85' = 1°25', the final answer is 1°25'57" (rounding).
• Sub-chord vs. full chord tangential angles: The first and last chords of a curve are often shorter "sub-chords" (to align with even station points), requiring this same formula but with their own (shorter) chord length, while intermediate full chords use the standard chord length consistently throughout the rest of the curve.