Answer: In a triangle, the sum of the angles is 180 degrees. Therefore, if we know two of the angles, we can use this property to find the measure of the third angle.
In this case, we are given angle B = 27 degrees and we want to find the measure of angle C. We can use the following equation to find angle C:
Angle B + Angle C + Angle A = 180
27 + Angle C + 90 = 180
Angle C = 180 - 27 - 90
Angle C = 63 degrees
Additionally, we can use the Law of Cosines to find the measure of angle C.
c² = a² + b² - 2ab * cos(C)
c² = 28² + 18² - 2 * 28 * 18 * cos(C)
c² = 784 + 324 - 1008 * cos(C)
c = √(1108 - 1008*cos(C))
We know that cos(C) = (a² + b² - c²) / 2ab
cos(C) = (784 + 324 - c²) / (22818)
We can substitute the value of c² that we obtained from the first equation and find cos(C) and thus angle C.
So the measure of angle C is 63 degrees.
Explanation: