The given information is:
We know the measure of two sides and one angle.
We can apply the Sine Rule to solve this problem. This rule states:
[tex]\frac{\sin A}{\bar{BC}}=\frac{\sin C}{\bar{AB}}[/tex]
If we replace the known values, we can solve for angle A as follows:
[tex]\begin{gathered} \sin A=\frac{\sin C*BC}{AB}=\frac{\sin36\degree *24}{31} \\ \\ \sin A=\frac{0.59*24}{31} \\ \\ \sin A=0.455 \\ \\ A=\sin^{-1}(0.455) \\ \\ A\approx27\degree \end{gathered}[/tex]
The measure of angle A is approximately 27 degrees.
