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