Correct. Since Joe's path is the hypotenuse and Matt's path are the two legs of a right triangle, we can use the Pythagorean Theorem. If the hypotenuse is c, then $\displaystyle{a}={50}\usepackage{cmbright}\Huge\$ and $\displaystyle{b}={120}\usepackage{cmbright}\Huge\$ , so $\displaystyle{{c}}^{{2}}={{a}}^{{2}}+{{b}}^{{2}}={{50}}^{{2}}+{{120}}^{{2}}={2500}+{14400}={16900}\usepackage{cmbright}\Huge\$ . Therefore, the length of Joe's path is $\displaystyle{c}=\sqrt{{{16900}}}={130}\usepackage{cmbright}\Huge\$ feet.