1. The problem is to solve for $x$ in a right triangle with sides 8, 15, and 17, where $x$ is the angle opposite the side of length 8. 2. We use the sine function, which relates an angle to the ratio of the opposite side over the hypotenuse: $$\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. Here, the opposite side is 8 and the hypotenuse is 17, so $$\sin(x) = \frac{8}{17}$$ 4. To find $x$, take the inverse sine (arcsin) of both sides: $$x = \sin^{-1}\left(\frac{8}{17}\right)$$ 5. Calculate the value: $$x \approx \sin^{-1}(0.4706) \approx 28.07^\circ$$ 6. Therefore, the angle $x$ is approximately $28.07^\circ$.