1. **Problem statement:** We need to find the size of angle $x$ in a triangle with sides 15.3 mm, 13.86 mm, and 6.48 mm, where there is a right angle (90°) between the sides 6.48 mm and 13.86 mm. 2. **Identify the triangle type and sides:** Since there is a right angle between the sides 6.48 mm and 13.86 mm, these two sides are the legs of a right triangle, and the side opposite the right angle (hypotenuse) is 15.3 mm. 3. **Formula used:** To find angle $x$ between the sides 15.3 mm and 6.48 mm, we use the cosine definition in a right triangle: $$\cos(x) = \frac{\text{adjacent side}}{\text{hypotenuse}}$$ Here, the side adjacent to angle $x$ is 6.48 mm, and the hypotenuse is 15.3 mm. 4. **Calculate cosine of angle $x$:** $$\cos(x) = \frac{6.48}{15.3} \approx 0.4235$$ 5. **Find angle $x$ using inverse cosine:** $$x = \cos^{-1}(0.4235) \approx 64.9^\circ$$ 6. **Answer:** The size of angle $x$ is approximately **64.9 degrees** to 1 decimal place.