Convert the Bearing direction N 430 07’ W into decimal Azimuth format (write only the numeric answer with 3 decimals and no units)

Convert the Bearing direction S 30 13’ 48" W into decimal Azimuth format (write only a numeric answer with 2 decimals and no units)

The magnetic base of bearings for a closed traverse survey is  S 760 30’ W and the magnetic declination at the site is 20 45’ E. Determine it's True North Azimuth in decimal degrees (enter only the numerical answer).

The magnetic bearing of a boundary line was recorded as  N 330 15’ W and the magnetic declination at the time was 30 45’ W. Determine the True Azimuth direction of the boundary line in decimal degrees (enter only the numerical answer)

To find the component form of the vector \(\mathbf{v}\) with a magnitude of 4 and a bearing of 125°, we need to convert the polar coordinates (magnitude and direction) into Cartesian coordinates (components along the \(i\) and \(j\) directions). 1. **Convert the bearing to a standard angle:** Bearings are measured clockwise from the north direction. A bearing of 125° means the angle is 125° clockwise from the north. To convert this to a standard angle (measured counterclockwise from the positive x-axis), we use: \[ \text{Standard angle} = 360° - 125° = 235° \] 2. **Calculate the components:** The components of the vector can be found using trigonometry: \[ v_x = v \cos(\theta) \] \[ v_y = v \sin(\theta) \] where \(v\) is the magnitude and \(\theta\) is the standard angle. Given: \[ v = 4, \quad \theta = 235° \] Converting 235° to radians: \[ \theta = 235° \times \frac{\pi}{180°} = \frac{235\pi}{180} \approx 4.1015 \text{ radians} \] Now, calculate the components: \[ v_x = 4 \cos(235°) = 4 \cos(4.1015) \approx 4 \times (-0.5736) \approx -2.29 \] \[ v_y = 4 \sin(235°) = 4 \sin(4.1015) \approx 4 \times (-0.8192) \approx -3.28 \] 3. **Write the vector in component form:** \[ \mathbf{v} = v_x \mathbf{i} + v_y \mathbf{j} = -2.29\mathbf{i} - 3.28\mathbf{j} \] Therefore, the correct answer is: \[ \boxed{E} \]

If you measure an Azimuth of 213.2 with a magnetic compass, and the Magnetic Declination of your location is 7.2 degrees East, what is the True Azimuth (report in numerical DD format, with no units)