1. **State the problem:** We have a right triangle with vertices A, B, and C, where angle B is the right angle. The sides are AC = 24, BC = 10, and we want to find $\cos C$ as a fraction in simplest terms. 2. **Recall the definition of cosine in a right triangle:** $$\cos C = \frac{\text{adjacent side to angle C}}{\text{hypotenuse}}$$ 3. **Identify the sides relative to angle C:** - The side adjacent to angle C is BC = 10. - The hypotenuse is side AB, which we need to find. 4. **Find the hypotenuse AB using the Pythagorean theorem:** $$AB = \sqrt{AC^2 + BC^2} = \sqrt{24^2 + 10^2} = \sqrt{576 + 100} = \sqrt{676} = 26$$ 5. **Calculate $\cos C$:** $$\cos C = \frac{BC}{AB} = \frac{10}{26}$$ 6. **Simplify the fraction:** $$\cos C = \frac{\cancel{10}}{\cancel{26}} = \frac{5}{13}$$ **Final answer:** $$\cos C = \frac{5}{13}$$