1. **State the problem:** We need to find the size of angle $x^\circ$ in a right triangle where the side opposite to angle $x$ is 16 and the adjacent side is 13. 2. **Formula used:** In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side: $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** $$\tan(x) = \frac{16}{13}$$ 4. **Calculate the angle:** To find $x$, take the arctangent (inverse tangent) of both sides: $$x = \tan^{-1}\left(\frac{16}{13}\right)$$ 5. **Evaluate the arctangent:** Using a calculator, $$x \approx \tan^{-1}(1.2308) \approx 50.19^\circ$$ 6. **Round to the nearest degree:** $$x \approx 50^\circ$$ **Final answer:** The size of angle $x$ is approximately $50^\circ$.