Given data:
* The distance traveled by Greg towards the north is d_1 = 10 km.
* The distance traveled by Greg towards the west is d_2 = 7 km.
Solution:
The displacement of Greg from the home to the restaurant is,
[tex]D=\sqrt[]{d^2_1+d^2_2}[/tex]Substituting the known values,
[tex]\begin{gathered} D=\sqrt[]{10^2+7^2} \\ D=\sqrt[]{100+49} \\ D=\sqrt[]{149} \\ D=12.2\text{ km} \end{gathered}[/tex]Thus, the restaurant is at the displacement of 12.2 km from the home.
The direction of the restaurant is,
[tex]\begin{gathered} \tan (\theta)=\frac{10}{7} \\ \tan (\theta)=1.43 \\ \theta=55^{\circ} \end{gathered}[/tex]Thus, the restaurant from home is north of the west direction making an angle of 55 degrees with the west.
