1. **State the problem:** We have a right triangle ABC with right angle at C. Given sides: hypotenuse AB = 53, opposite side BC = 28, adjacent side AC = 45. We need to find the ratios for $\sin A$, $\cos A$, and $\tan A$ in reduced form. 2. **Recall the definitions:** - $\sin A = \frac{\text{opposite}}{\text{hypotenuse}}$ - $\cos A = \frac{\text{adjacent}}{\text{hypotenuse}}$ - $\tan A = \frac{\text{opposite}}{\text{adjacent}}$ 3. **Calculate $\sin A$:** $$\sin A = \frac{28}{53}$$ Since 28 and 53 have no common factors (53 is prime), this fraction is already simplified. 4. **Calculate $\cos A$:** $$\cos A = \frac{45}{53}$$ 45 and 53 share no common factors, so this is simplified. 5. **Calculate $\tan A$:** $$\tan A = \frac{28}{45}$$ 28 and 45 share no common factors, so this is simplified. **Final answers:** - $\sin A = \frac{28}{53}$ - $\cos A = \frac{45}{53}$ - $\tan A = \frac{28}{45}$