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Link traverse XP to TY, angles to right

Short answer

Angular misclosure is +0°45′. Adjusted bearings: XP 148°15′, PQ 60°54′, QR 109°33′, RS 44°57′, ST 277°51′, TY 36°45′.

The following angles to the right were obtained in a closed link traverse between two adjusted known lines XP and TY. Compute the angular misclosure, if any, on that traverse and the adjusted bearings of the traverse lines.

StationAngle to the rightBearing
X
P92°30′148°15′
Q228°30′
R115°15′
S52°45′
T298°45′
Y36°45′

Reading of the table: 148°15′ is the adjusted bearing of the known line XP and 36°45′ is the adjusted bearing of the known line TY. Angles are measured to the right at P, Q, R, S, T, so the bearing of the next line = bearing of the previous line + 180° + angle.

Rule (angles to the right): FB of next line=FB of previous line+180∘+angle to the right\text{FB of next line} = \text{FB of previous line} + 180^\circ + \text{angle to the right} (add or subtract 360∘360^\circ to bring the result between 0∘0^\circ and 360∘360^\circ).

Step 1: Bearings computed from the observed angles

LineWorkingComputed FB
XPgiven148°15′
PQ148°15′ + 180° + 92°30′ − 360°60°45′
QR60°45′ + 180° + 228°30′ − 360°109°15′
RS109°15′ + 180° + 115°15′ − 360°44°30′
ST44°30′ + 180° + 52°45′277°15′
TY277°15′ + 180° + 298°45′ − 720°36°00′

Computed FB of TY = 36°00′; given (observed) FB of TY = 36°45′.

Step 2: Angular misclosure

Misclosure=given−computed=0∘45′\text{Misclosure} = \text{given} - \text{computed} = 0^\circ 45'

The computed bearing of TY is 36°00′ against the known 36°45′: angular misclosure = +0°45′ (the computed bearing is 45′ less than the known one). It is distributed equally among the 5 angles (+9′ each).

Step 3: Adjustment

Total correction = +0°45′ (added to the computed bearing of the last line). It is distributed equally over the 5 observed angles: +0°45′ / 5 = +0°09′ per angle. The correction to a line is +0°09′ multiplied by the number of angles used to reach it.

LineComputed FBCorrectionCorrected FBCorrected BB
XP148°15′0148°15′328°15′
PQ60°45′+0°09′60°54′240°54′
QR109°15′+0°18′109°33′289°33′
RS44°30′+0°27′44°57′224°57′
ST277°15′+0°36′277°51′97°51′
TY36°00′+0°45′36°45′216°45′

Check: corrected FB of the last line equals the observed value 36°45′.

Answer: angular misclosure = +0°45′. Adjusted bearings: XP 148°15′, PQ 60°54′, QR 109°33′, RS 44°57′, ST 277°51′, TY 36°45′.

✓ Answer checked by Claude Opus 5.5 (high effort)

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