Theodolite Surveying Questions and Answers

Answer: D

The whole circle bearing is 145°.

A positive departure means the line goes east, and a negative latitude means it goes south, so the line lies in the south-east quadrant (between 90° and 180°). The reduced bearing from south is

\[ \tan^{-1}\frac{70.03}{100} \approx 35^{\circ} \]

so the whole circle bearing, measured clockwise from north, is \(180^{\circ} - 35^{\circ} = 145^{\circ}\). 55° and 125° are \(90^{\circ} \mp 35^{\circ}\), which measure from the east-west line, and 135° would need equal departure and latitude.

Answer: C

The whole circle bearing is about 152 degrees.

A positive departure means the line runs east and a negative latitude means it runs south, so it lies in the south-east quadrant. The reduced bearing is measured from south towards east:

\[ \begin{aligned} \theta &= \tan^{-1}\frac{70}{130} = 28.3^{\circ} \\ WCB &= 180^{\circ} - 28.3^{\circ} = 151.7^{\circ} \approx 152^{\circ} \end{aligned} \]

28 is the reduced bearing S 28 E, not the whole circle bearing measured clockwise from north. 62 is the angle measured from the east-west line instead, and 208 puts the line in the south-west quadrant, which would need a negative departure.