Step 1
Draw the triangle
Step 2
Find the area of the triangle
[tex]\begin{gathered} Find\text{ side XY} \\ z^2=y^2+x^2-2xy\cos Z \\ z^2=11^2+8^2-2(11)(8)\cos 31 \\ z^2=121+64-176\cos \mleft(31^{\circ\: }\mright) \\ z^2=-176\cos \mleft(31^{\circ\: }\mright)+185 \\ z=5.842820815 \end{gathered}[/tex]
Step 3
Find the area
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ s=\frac{11+8+5.842820815}{2}=12.42141041 \\ A=\sqrt[]{12.42141041(12.42141041-11)(12.42141041-8)(12.42141041-5.842820815)} \\ A=22.661675295946unit^2 \\ A\approx22.7\text{unit}^2\text{ to the nearest tenth} \end{gathered}[/tex]
Answer; Area=22.7units squared to the nearest tenth
