Corrected bearings, closed link traverse T1-T2

The bearings of the first line (T1A) and the last line (ET2) are known (corrected). The bearing of ET2 is computed through the five angles to the right at A, B, C, D and E, and compared with its known value.

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

Step 1: Bearings computed from the observed angles

Computed FB of E-T2 = 57°32′57″; given (known) FB of E-T2 = 57°32′52″.

Step 2: Angular misclosure

$$\text{Misclosure} = \text{given} - \text{computed} = -0^\circ 00'05''$$

The computed bearing is 5″ too large. The misclosure is small (a few seconds), so it is distributed equally among the five angles.

Step 3: Adjustment

Total correction = −0°00′05″ (added to the computed bearing of the last line). It is distributed equally over the 5 observed angles: −0°00′05″ / 5 = −0°00′01″ per angle. The correction to a line is −0°00′01″ multiplied by the number of angles used to reach it.

Check: the corrected FB of the last line equals the given value 57°32′52″.

Answer: angular misclosure = −5″ (known − computed; the computed bearing is 5″ too large). Corrected bearings: T1A 310°17′20″, AB 42°57′19″, BC 130°24′46″, CD 37°27′16″, DE 327°02′54″, ET2 57°32′52″.