The following PRS92 geographic and grid coordinated of station JLZ-31 and AJR-2 are provided as project control stations.
| Station |
Latitude |
Longitude |
Northing |
Easting |
| JLZ-31 |
10°50’20.57″ |
122°36’30.79″ |
1198555.068 |
457197.963 |
| AJR-2 |
10°41’24.76″ |
122°31’14.59″ |
1182106.743 |
447568.005 |
- Determine the grid azimuth from station AJR-2 to station JLZ-31.
- Determine the meridian convergence, in seconds.
- Determine the geodetic azimuth from station AJR-2 to station JLZ-31, assuming that the arc to chord coordinates is negligible.
\[
\Delta N = 1182106.743 – 1198555.068 = 16448.325
\]
\[
\Delta E = 447568.005 – 457197.963 = 9629.958
\]
\[
\beta = \arctan \frac{\Delta E}{\Delta N}
\]
\[
\beta = \arctan \frac{9629.958}{16448.325}
\]
\[
\beta = 30^{\circ}20’51.29″
\]
\[
\text {Grid Azimuth} = 180^{\circ} + 30^{\circ}20’51.29″
\]
\[
\text {Grid Azimuth} = 210^{\circ}20’51.29″ \leftarrow \text{answer}
\]
\[
\alpha = \Delta \lambda \sin \phi_{mean}
\]
\[
\Delta \lambda = 122°36’30.79″ – 122°31’14.59″ = 0^{\circ}5’16.2″
\]
\[
\phi_{mean} = \frac{10^{\circ}50’20.57″ + 10^{\circ}41’24.76″}{2} = 10^{\circ}45’52.66″
\]
\[
\alpha = 0^{\circ}5’16.2″ \sin 10^{\circ}45’52.66″
\]
\[
\alpha = 59.06″ \leftarrow \text{answer}
\]
\[
\text {Geodetic Azimuth} = \text {Grid Azimuth} \pm \alpha
\]
\[
\text {Geodetic Azimuth} = 210^{\circ}20’51.29″ + 59.06″
\]
\[
\text {Geodetic Azimuth} = 210^{\circ}21’50.35″ \leftarrow \text{answer}
\]
