Hello!
To find the measure of side a, you need to use the Law of Sines. This law states, sin A / a = sin B / b = sin C / c. Since we are given two angle measures and the measure of a side, we can use this law.
Here are the given values: sin C = 102 degrees, sin B = 28 degrees, b = 27 cm.
We also need to find the the value of sin A, and to do that, triangles are always equal to 180 degrees, and since we are given two angles, we can subtract those two angles from 180.
180 - 102 - 28 = 55 The measure of sin A = 55 degrees.
sin (28) / 27 = sin (55) / a (multiply both sides by a)
0.017387... · a = 0.81915... (divide both sides by 0.017387...)
c = 47.11278...
The measure of side a is equal to about 47.1 degrees.