1. The problem asks to write the ratios equal to $\sin A$ and $\cos A$ for the given right triangle. 2. Recall the definitions for sine and cosine in a right triangle: - $\sin \theta = \frac{\text{opposite side}}{\text{hypotenuse}}$ - $\cos \theta = \frac{\text{adjacent side}}{\text{hypotenuse}}$ 3. From the triangle, angle $A$ is at vertex $C$. The hypotenuse is side $AC = 20$. 4. Identify the sides relative to angle $A$: - Opposite side to angle $A$ is $AB = 16$ - Adjacent side to angle $A$ is $BC = 12$ 5. Write the ratios: - $\sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{16}{20}$ - $\cos A = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{12}{20}$ 6. Simplify the fractions: - $\sin A = \frac{\cancel{16}}{\cancel{20}} = \frac{4}{5}$ - $\cos A = \frac{\cancel{12}}{\cancel{20}} = \frac{3}{5}$ 7. Final answer: $$\sin A = \frac{4}{5}, \quad \cos A = \frac{3}{5}$$