1. **State the problem:** We need to find the hypotenuse $c$ of a right triangle where side $a = 64.1$ cm and angle $B = 58.2^\circ$. The triangle is labeled such that $C = 90^\circ$. 2. **Recall the triangle properties:** In a right triangle, the hypotenuse is opposite the right angle $C$. Given angle $B$ and side $a$ (which is adjacent to angle $B$), we can use trigonometric ratios to find $c$. 3. **Use the cosine formula:** Cosine relates the adjacent side and hypotenuse: $$\cos(B) = \frac{a}{c}$$ 4. **Rearrange to solve for $c$:** $$c = \frac{a}{\cos(B)}$$ 5. **Substitute the known values:** $$c = \frac{64.1}{\cos(58.2^\circ)}$$ 6. **Calculate $\cos(58.2^\circ)$:** $$\cos(58.2^\circ) \approx 0.527$$ 7. **Calculate $c$:** $$c = \frac{64.1}{0.527} \approx 121.6$$ 8. **Answer with units and rounding:** The hypotenuse $c$ is approximately $121.6$ cm. **Final answer:** $c = 121.6$ cm