1. We are asked to find $\sin(c)$ in a right triangle where the hypotenuse is 75, the side opposite angle $c$ is 21, and the adjacent side to angle $c$ is 72. 2. Recall the definition of sine in a right triangle: $$\sin(c) = \frac{\text{opposite side}}{\text{hypotenuse}}$$ 3. Substitute the given values: $$\sin(c) = \frac{21}{75}$$ 4. Simplify the fraction by dividing numerator and denominator by 3: $$\sin(c) = \frac{7}{25}$$ 5. To express as a decimal rounded to three decimal places: $$\sin(c) \approx 0.280$$ 6. Therefore, the sine of angle $c$ is $\frac{7}{25}$ or approximately 0.280.