Triangle abc has side a = 12, b = 16,
and c = 19.
find the measure of angle c to the nearest whole number.

When a triangle has three known sides and you want to find one angle, you can use the cosine law. The formula is

c^2 = b^2 + a^2 - 2abcosC
(19)^2 = (16)^2 + (12)^2 -2(12)(16)cosC
2(12)(16)cosC = (16)^2 + (12)^2 - (19)^2
384cosC = 39
cos C = 39/384
cos C = 0.1016
c = arccosine 0.1016
c = 84.17 degrees = 84 degrees