Bearing Azimuth 17F727

1. **Stating the problem:** We need to solve parts $a$ and $b$ involving a line segment's bearing, azimuth, and back azimuth angles. 2. **Understanding the terms:** - The **bearing** is the direction of a line segment measured clockwise from the north. - The **azimuth** is the angle measured clockwise from the north direction to the line segment. - The **back azimuth** is the azimuth of the line segment in the opposite direction, which is the azimuth plus or minus $180^\circ$. 3. **Formula for back azimuth:** $$\text{Back Azimuth} = \begin{cases} \text{Azimuth} + 180^\circ, & \text{if Azimuth} < 180^\circ \\ \text{Azimuth} - 180^\circ, & \text{if Azimuth} \geq 180^\circ \end{cases}$$ 4. **Part a: Calculate the azimuth and bearing of the line segment.** - Suppose the line segment has coordinates or directions given (not specified in the prompt). - The azimuth is measured clockwise from north. - The bearing is expressed as $N$ or $S$ followed by the angle east or west. 5. **Part b: Calculate the back azimuth.** - Use the formula above to find the back azimuth. 6. **Example (assuming azimuth $120^\circ$):** - Back azimuth $= 120^\circ + 180^\circ = 300^\circ$ 7. **Summary:** - Bearing and azimuth describe the direction of a line segment. - Back azimuth is the opposite direction, found by adding or subtracting $180^\circ$. Since no specific values or coordinates were provided, this is the general method to solve parts $a$ and $b$.