Answer:
[tex]24.269\ \text{cm}[/tex]
Step-by-step explanation:
[tex]m\angle A=120^{\circ}[/tex]
[tex]b=13\ \text{cm}[/tex]
[tex]c=15\ \text{cm}[/tex]
From the law of cosines we know that
[tex]a^2=b^2+c^2-2bc\cos A\\\Rightarrow a=\sqrt{b^2+c^2-2bc\cos A}\\\Rightarrow a=\sqrt{13^2+15^2-2\times 13\times 15\cos120^{\circ}}\\\Rightarrow a=24.269\ \text{cm}[/tex]
The side [tex]a[/tex] of the triangle is [tex]24.269\ \text{cm}[/tex].
