1. **State the problem:** We need to find $\sin(x^\circ)$ for a right triangle where the opposite side to angle $x$ is 7, the adjacent side is 24, and the hypotenuse is 25. 2. **Recall the formula:** Using SOH-CAH-TOA, sine is defined as the ratio of the opposite side to the hypotenuse: $$\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Substitute the values:** $$\sin(x) = \frac{7}{25}$$ 4. **Simplify:** The fraction $\frac{7}{25}$ is already in simplest form since 7 and 25 have no common factors other than 1. 5. **Final answer:** $$\sin(x) = \frac{7}{25}$$ This means the sine of angle $x$ is $\frac{7}{25}$, which is approximately 0.28 if you want a decimal approximation.