Solution:
Given:
[tex]\begin{gathered} \text{Latitude}=30^003^{\prime}45.47^{\doubleprime} \\ \text{Longitude}=31^014^{\prime}58.81^{\doubleprime} \end{gathered}[/tex]
Recall that;
[tex]\begin{gathered} x-\text{coordinate}=\cos (\text{latitude)}-\cos (\text{longitude)} \\ y-\text{coordinate}=\cos (\text{latitude)}-sin(\text{longitude)} \\ z-\text{coordinate}=\sin (\text{latitude)} \end{gathered}[/tex]
Converting the latitude and longitude to degrees,
[tex]\begin{gathered} 30^003^{\prime}45.47^{\doubleprime}=30+\frac{3}{60}+\frac{45.47}{3600} \\ latitude=30^003^{\prime}45.47^{\doubleprime}=30.06263^0\approx30.06^0 \\ \\ \\ \text{Also,} \\ 31^014^{\prime}58.81^{\doubleprime}=31+\frac{14}{60}+\frac{58.81}{3600} \\ longitude=31^014^{\prime}58.81^{\doubleprime}=31.24967^0\approx31.25^0 \end{gathered}[/tex]
Hence,
[tex]\begin{gathered} x-\text{coordinate}=\cos (\text{latitude)}-\cos (\text{longitude)} \\ x-\text{coordinate}=\cos 30.06-\cos 31.25 \\ x-\text{coordinate}=0.8655-0.8549 \\ x-\text{coordinate}=0.0106 \\ x\approx0.01 \end{gathered}[/tex]
Also,
[tex]\begin{gathered} y-\text{coordinate}=\cos (\text{latitude)}-sin(\text{longitude)} \\ y-\text{coordinate}=\cos 30.06-\sin 31.25 \\ y-\text{coordinate}=0.8655-0.5188 \\ y-\text{coordinate}=0.3467 \\ y\approx0.35 \end{gathered}[/tex]
And,
[tex]\begin{gathered} z-\text{coordinate}=\sin (\text{latitude)} \\ z-\text{coordinate}=\sin 30.06 \\ z-\text{coordinate}=0.5009 \\ z\approx0.50 \end{gathered}[/tex]
Therefore, the solution is;
