To find the length of each side, we use the distance formula.
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2_{}}[/tex]
Let's find side CS first. The points are C(0,0) and S(-5,7). So, the coordinates are
[tex]x_1=0,x_2=-5,y_1=0,y_2=7[/tex]
Use the coordinates to find the length of CS.
[tex]\begin{gathered} CS=\sqrt[]{(7-0)^2+(-5-0)^2}=\sqrt[]{7^2+(-5)^2} \\ CS=\sqrt[]{49+25}=\sqrt[]{74} \end{gathered}[/tex]
Therefore, the length of CS is
[tex]CS=\sqrt[]{74}[/tex]
Let's repeat the same process for CT and CU. Given that C is just (0,0), we can use just T and U as coordinates.
[tex]CT=\sqrt[]{3^2+(-6)^2}=\sqrt[]{9+36}=\sqrt[]{45}=\sqrt[]{9\cdot5}=3\sqrt[]{5}[/tex]
Therefore, the length of CT is
[tex]CT=3\sqrt[]{5}[/tex]
Let's do the process one more time for CU.
[tex]CU=\sqrt[]{1^2+(-8)^2}=\sqrt[]{1+64}=\sqrt[]{65}[/tex]
Therefore, the length of CU is
[tex]CU=\sqrt[]{65}[/tex]
