In this problem, we were given a triangle with the measurements for two of its sides and one angle. We need to use the available information, to determine the value of the angle C in degrees.
For that, we will use the law of sines, which is shown below:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]
Where A, B, C are the angles for the triangle, and a, b, c are the opposite side from those angles.
We need to find the value of angle C, and we have angle A, therefore we will use:
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex]
Replacing the data from the problem on the expression above, we obtain:
[tex]\begin{gathered} \frac{\sin(70)}{15}=\frac{\sin C}{14} \\ \sin C=\frac{14}{15}\cdot\sin (70) \\ \arcsin (\sin C)=\arcsin (\frac{14}{15}\cdot\sin (70)) \\ C=61.29º \end{gathered}[/tex]
The value of angle C is approximately 61.3°
