1. **State the problem:** We need to find the angle $x$ in a right triangle with a right angle at $P$. The side opposite angle $x$ (OP) is 56, and the side adjacent to angle $x$ (PQ) is 42. 2. **Formula used:** To find an angle when we know the opposite and adjacent sides, we use the tangent function: $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** $$\tan(x) = \frac{56}{42}$$ 4. **Simplify the fraction:** $$\tan(x) = \frac{\cancel{56}}{\cancel{42}} = \frac{56 \div 14}{42 \div 14} = \frac{4}{3}$$ 5. **Find the angle $x$ by taking the arctangent (inverse tangent):** $$x = \tan^{-1}\left(\frac{4}{3}\right)$$ 6. **Calculate the value:** Using a calculator, $$x \approx 53.1^\circ$$ 7. **Final answer:** $$x \approx 53.1^\circ$$ This means the angle $x$ is approximately 53.1 degrees.