For this problem, we are given two sides and one angle of a triangle. We need to determine the length of the side that is opposite to the known angle.
To solve this problem, we need to use the law of cosines.
[tex]a=\sqrt{b^2+c^2-2bc\cdot\cos(m\angle A)}[/tex]
Applying the given data, we have:
[tex]\begin{gathered} a=\sqrt{13^2+21^2-2\cdot13\cdot21\cdot\cos(105)}\\ \\ a=\sqrt{169+441-546\cdot(-0.2588)}\\ \\ a=\sqrt{610+141.3048}\\ \\ a=\sqrt{751.3048}=27.41 \end{gathered}[/tex]
The correct answer is 27.4.
