1. **State the problem:** We have a right triangle with a 45° angle and hypotenuse length 13. We want to find the correct trigonometric equation to solve for the side length $x$ adjacent to the 45° angle. 2. **Recall the trigonometric definitions:** - $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ - $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$ - $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ 3. **Identify the sides:** - Angle $\theta = 45^\circ$ - Hypotenuse = 13 - Adjacent side to $45^\circ$ is $x$ 4. **Apply the cosine formula since $x$ is adjacent:** $$\cos 45^\circ = \frac{x}{13}$$ 5. **Check other options:** - $\sin 45^\circ = \frac{x}{13}$ is incorrect because $x$ is adjacent, not opposite. - $\sin 45^\circ = \frac{13}{x}$ is incorrect because hypotenuse cannot be opposite side. - $\tan 45^\circ = \frac{x}{13}$ is incorrect because tangent relates opposite over adjacent, and $x$ is adjacent. 6. **Final answer:** $$\boxed{\cos 45^\circ = \frac{x}{13}}$$