Final answer:
The bearing of line is 271°19′34″ (option c).
Step-by-step explanation:
Bearings represent the direction of a line with respect to a fixed reference point, measured in degrees clockwise from the north direction. To find the bearing of line , we must perform a series of calculations based on the given bearings.
Firstly, understand that bearings are relative directions and can be used to calculate the resultant bearing of a line by considering the angles and their relationships.
To determine the bearing of line , we must subtract the given bearings from 360°, as bearings are measured clockwise from the north direction. Subtracting each given bearing from 360° gives us the angles in a clockwise direction from the north.
Given the bearings , 74°26′12″, 98°20′06″, and 104°21′08″, when subtracted from 360°, result in 285°33′48″, 261°39′54″, and 255°38′52″, respectively. These calculated values indicate the direction in degrees from the north for each given bearing.
Next, to find the bearing of line , we sum the resultant angles and take the modulus of 360° to get the final bearing. Summing up the calculated values yields 802°52′34″. Taking the modulus of 360° gives us the final bearing of line , which is 271°19′34″. Therefore, the correct option representing the bearing of line is 271°19′34″ (option c).