1. **State the problem:** We have a right triangle with legs 20 and 48, and hypotenuse 52. We want to find the angle $x$ opposite the leg of length 20. 2. **Formula used:** To find an angle in a right triangle, we use the sine function: $$\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}$$ Here, opposite side = 20, hypotenuse = 52. 3. **Calculate sine of angle $x$:** $$\sin(x) = \frac{20}{52}$$ 4. **Simplify the fraction:** $$\sin(x) = \frac{\cancel{4}5}{\cancel{4}13} = \frac{5}{13}$$ 5. **Find angle $x$ using inverse sine:** $$x = \sin^{-1}\left(\frac{5}{13}\right)$$ 6. **Evaluate the inverse sine:** Using a calculator or tables, $$x \approx 22.62^\circ$$ **Final answer:** $$x \approx 22.62^\circ$$