1. **State the problem:** We have a right triangle ABC with a right angle at A, hypotenuse BC = 6, and angle B = 60°. 2. **Identify what to find:** We need to find the lengths AC and AB, and the measure of angle C. 3. **Recall the properties of right triangles:** The sum of angles in a triangle is 180°. Since angle A = 90° and angle B = 60°, angle C = 180° - 90° - 60° = 30°. 4. **Use trigonometric ratios:** In right triangle ABC, with hypotenuse BC = 6, - AC is opposite angle B (60°), - AB is adjacent to angle B (60°). 5. **Calculate AC using sine:** $$AC = BC \times \sin(60^\circ) = 6 \times \frac{\sqrt{3}}{2} = 3\sqrt{3}$$ 6. **Calculate AB using cosine:** $$AB = BC \times \cos(60^\circ) = 6 \times \frac{1}{2} = 3$$ 7. **Final answers:** - $AC = 3\sqrt{3}$ - $AB = 3$ - $m\angle C = 30^\circ$