Given the information on the problem, we can use the law of cosines to find the length of p with the following equation:
[tex]p^2=q^2+o^2-2q\cdot o\cdot\cos P[/tex]substituting the values at hand, we get the following:
[tex]\begin{gathered} p^2=(18)^2+(96)^2-2(18)(96)\cos 142 \\ \Rightarrow p^2=324+9216+2723.37 \\ \Rightarrow p^2=12263.37 \\ \Rightarrow p=\sqrt[]{12263.37}=110.74 \\ p=110.7\operatorname{cm} \end{gathered}[/tex]therefore, the length of p is 111 cm
