Question

Please show all work Location - cairo EgyptLatitude = 30 03 45.47Longitude = 31 14 58.81

Answer 1

Given:

`\begin{gathered} \text{Latitude}=30^003^(\prime)45.47^(\doubleprime) \\ \text{Longitude}=31^014^(\prime)58.81^(\doubleprime) \end{gathered}`

Recall that;

`\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}`

Converting the latitude and longitude to degrees,

`\begin{gathered} 30^003^(\prime)45.47^(\doubleprime)=30+(3)/(60)+(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+(14)/(60)+(58.81)/(3600) \\ longitude=31^014^(\prime)58.81^(\doubleprime)=31.24967^0\approx31.25^0 \end{gathered}`

Hence,

`\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}`

Also,

`\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}`

And,

`\begin{gathered} z-\text{coordinate}=\sin (\text{latitude)} \\ z-\text{coordinate}=\sin 30.06 \\ z-\text{coordinate}=0.5009 \\ z\approx0.50 \end{gathered}`

Therefore, the solution is;