5) Triangle ABC with hypotenuse AB = 10, side BC = 6, and angle C = 90 degrees. Calculate cos A, cos B, sin A, sin B, tan A, tan B.

1. Use the Pythagorean theorem to find side AC: AC = sqrt(AB² - BC²) = sqrt(10² - 6²) = sqrt(100 - 36) = sqrt(64) = 8.
2. Calculate the trigonometric functions:
cos A = AC/AB = 8/10 = 0.8
cos B = BC/AB = 6/10 = 0.6
sin A = BC/AB = 6/10 = 0.6
sin B = AC/AB = 8/10 = 0.8
tan A = BC/AC = 6/8 = 0.75
tan B = AC/BC = 8/6 = 4/3 ≈ 1.33
3. The values are: cos A = 0.8, cos B = 0.6, sin A = 0.6, sin B = 0.8, tan A = 0.75, tan B = 4/3.