Final answer:
To find the measures of angles A and C, use the cosine function and the sum of the measures of angles in a triangle. To find the length of AC, use the Pythagorean theorem.
Step-by-step explanation:
To find the measures of angles A and C, we first need to find the measure of angle A. Since angle B is a right angle, we know that the sum of the measures of angles A and C must be equal to 90 degrees. Therefore, m∠A = 90° - m∠C. Next, we can use the cosine function to find the measure of angle C. Since cos(C) = 15/17, we can take the inverse cosine of 15/17 to find the measure of angle C.
Once we have the measures of angles A and C, we can use the fact that the sum of the measures of angles in a triangle is 180 degrees to find the measure of angle B. Since m∠B = 90°, we can subtract the measures of angles A and C from 180 to find the measure of angle B.
Finally, to find the length of AC, we can use the Pythagorean theorem. Since AB = 16 units and triangle ABC is a right triangle, we can use the theorem to find the length of AC.