Hello!
To find the measure of line c, we can use the Law of Sines. This law states,
sin A / a = sin B / b = sin C / c.
Since you are given two angles, which is sin C, and sin A, and a side measure of triangle, which is side a = 8cm, you can substitute values into the formula:
sin A / a = sin C / c, to find the value of c.
sin (55) / 8 = sin (82) / c (multiply both sides by c)
0.10239.. ·c = 0.99026... (divide both sides by 0.10239...)
c = 9.6711...
The measure of side c is equal to about 9.7 centimeters.
