The measure of angle C in triangle ABC is approximately 53.13°. The closest answer choice is 43.5°.
Given that triangle ABC is a right triangle, we can use the trigonometric relation for sine to determine the measure of angle C.
Sin(C) = BA/CA = 12/15 = 0.8
Using the inverse sine function (arcsin), we can find the angle whose sine equals 0.8.
C = arcsin(0.8) ≈ 53.13°
Therefore, the measure of angle C in triangle ABC is approximately 53.13°. However, the answer choices require rounding to the nearest tenth of a degree. The closest answer choice is 43.5°.