1. We are given a right triangle with one leg of length 2.0 and a hypotenuse of length 6.2. We need to find the angle $x$ opposite the side of length 2.0. 2. To find angle $x$, we use the sine function, which relates the opposite side and the hypotenuse in a right triangle: $$\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. Substitute the known values: $$\sin(x) = \frac{2.0}{6.2}$$ 4. Simplify the fraction: $$\sin(x) = \frac{\cancel{2.0}}{\cancel{6.2}} \approx 0.3226$$ 5. To find $x$, take the inverse sine (arcsin) of 0.3226: $$x = \sin^{-1}(0.3226)$$ 6. Calculate the value (rounding to the nearest degree): $$x \approx 19$$ Therefore, the value of $x$ is approximately 19 degrees.