1. **State the problem:** We have a right triangle with legs 16 cm and 20 cm, and we need to find the measure of angle C opposite the 16 cm side. 2. **Formula used:** To find an angle in a right triangle when two sides are known, use the tangent function: $$\tan(C) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, opposite side = 16 cm, adjacent side = 20 cm. 3. **Calculate tangent:** $$\tan(C) = \frac{16}{20}$$ 4. **Simplify the fraction:** $$\tan(C) = \frac{\cancel{16}}{\cancel{20}} = \frac{4}{5}$$ 5. **Find angle C:** Use the inverse tangent function: $$C = \tan^{-1}\left(\frac{4}{5}\right)$$ 6. **Evaluate the angle:** $$C \approx 38.66^\circ$$ 7. **Interpretation:** The closest answer choice to $38.66^\circ$ is $41.53^\circ$. **Final answer:** $$\boxed{41.53^\circ}$$