Answer:
The length of x is;
[tex]42.8\text{ cm}[/tex]Explanation:
Given the figure in the attached image;
The length of the sides and angle of the triangle are give as;
[tex]\begin{gathered} a=35.2\text{ cm} \\ c=31.9\text{ cm} \\ m\angle B=79^{\circ} \end{gathered}[/tex]Recall that the law of cosines can be expressed as;
[tex]c^2=a^2+b^2-2ab\cos C[/tex]Since in this case we want to calculate b=AC=x;
[tex]\begin{gathered} b^2=a^2+c^2-2ac\cos B \\ b=\sqrt[]{a^2+c^2-2ac\cos B} \\ x=\sqrt[]{a^2+c^2-2ac\cos B} \end{gathered}[/tex]Substituting the given values;
[tex]\begin{gathered} x=\sqrt[]{a^2+c^2-2ac\cos B} \\ x=\sqrt[]{35.2^2+31.9^2-2(35.2)(31.9)\cos 79^{\circ}} \\ x=\sqrt[]{35.2^2+31.9^2-2(35.2)(31.9)\cos79^{\circ}} \\ x=\sqrt[]{1828.1387905} \\ x=42.7567 \\ x=42.8\text{ cm} \end{gathered}[/tex]Therefore, the length of x is;
[tex]42.8\text{ cm}[/tex]