1. **State the problem:** Given a right triangle with one angle measuring 35° and the side adjacent to this angle is 10 units long, find the length of the hypotenuse $x$. 2. The triangle is positioned so that the right angle is at the top-right corner, and the side adjacent to the 35° angle is the horizontal leg with length 10 units. 3. Recall that in a right triangle, the cosine of an angle equals the adjacent side over the hypotenuse. 4. Write the formula for $\cos(35^\circ)$: $$ \cos(35^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{10}{x} $$ 5. Solve for $x$ (the hypotenuse): $$ x = \frac{10}{\cos(35^\circ)} $$ 6. Calculate $\cos(35^\circ)$ using a calculator: $$ \cos(35^\circ) \approx 0.8192 $$ 7. Substitute this value back into the equation: $$ x = \frac{10}{0.8192} \approx 12.21 $$ 8. **Final answer:** The length of the hypotenuse $x$ is approximately 12.21 units.