Explanation
the law of cosines states that
[tex]\begin{gathered} a^2=b^2+c^2-2bc*cos(A) \\ b^2=a^2+c^2-2ac*cos(B) \\ c^2=a^2+b^2-2ab*cos(C) \end{gathered}[/tex]
so
Step 1
a) let
[tex]\begin{gathered} a=x \\ A=135 \\ b=31 \\ c=22 \end{gathered}[/tex]
now, replace in the proper equation, we are finding x (a), hence
[tex]\begin{gathered} a^{2}=b^{2}+c^{2}-2bccos(A) \\ x^2=31^2+22^2-2(31)(22)cos(135) \\ x^2=1445+964.49 \\ x^2=2409.4936 \\ square\text{ root in both sides} \\ \sqrt{x^2}=\sqrt{2409.49} \\ x=49.08659 \\ rounded \\ x=49.09 \end{gathered}[/tex]
so, the answer is
x=49.09
I hope this helps you
