Find the the measure of angle c

C = 72.97°

Step-by-step explanation:

Known side b (=13) is opposite known angle 47 deg, and

known side c (=17) is opposite unknown angle C.  This situation calls for the application of the Law of Sines:

    13              17

=

sin 47°       sin C

Solving this equation for sin C, we go through the following procedure:

Cross multiply, obtaining 13sin C = 17°sin 47°, or

             17sin 47°

sin C = = (17/13) sin 47° = 1.308 sin 47° = (1.308)(0.731)

                   13

Then sin C = 0.956

The angle C is equal to arcsin 0.956:  C = 72.97°

Then