1. **State the problem:** We need to find the length $m$ of the side opposite the $39^\circ$ angle in a right-angled triangle where the hypotenuse is 60. 2. **Formula used:** In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 39^\circ$, opposite side = $m$, hypotenuse = 60. $$\sin(39^\circ) = \frac{m}{60}$$ 4. **Solve for $m$:** Multiply both sides by 60: $$m = 60 \times \sin(39^\circ)$$ 5. **Calculate $\sin(39^\circ)$:** Using a calculator, $$\sin(39^\circ) \approx 0.6293$$ 6. **Find $m$:** $$m = 60 \times 0.6293 = 37.758$$ 7. **Round to 1 decimal place:** $$m \approx 37.8$$ **Final answer:** $m = 37.8$