1. **State the problem:** We have a right triangle with an angle of 37°, the hypotenuse length is 14, and the side opposite the 37° angle is labeled $x$. We want to find the value of $x$. 2. **Relevant formula:** 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, $\theta = 37^\circ$, opposite side = $x$, hypotenuse = 14, so: $$\sin(37^\circ) = \frac{x}{14}$$ 4. **Solve for $x$:** Multiply both sides by 14: $$x = 14 \times \sin(37^\circ)$$ 5. **Calculate $\sin(37^\circ)$:** Using a calculator or sine table, $$\sin(37^\circ) \approx 0.6018$$ 6. **Find $x$:** $$x = 14 \times 0.6018 = 8.4252$$ 7. **Final answer:** The length of the side opposite the 37° angle is approximately $$x \approx 8.43$$