1. **State the problem:** We need to find expressions that represent $\cos(46^\circ)$ based on the given right triangle. 2. **Recall the definition of cosine in a right triangle:** $$\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$$ where $\theta$ is the angle of interest. 3. **Identify the sides relative to the $46^\circ$ angle:** - Adjacent side length = 5 - Hypotenuse length = 7.25 4. **Calculate $\cos(46^\circ)$ using the triangle sides:** $$\cos(46^\circ) \approx \frac{5}{7.25}$$ 5. **Check the given choices:** - $\sin(44^\circ)$: Since $\sin(44^\circ) = \cos(46^\circ)$ (because $\sin(90^\circ - \theta) = \cos(\theta)$), this is a correct expression. - $\frac{20}{29}$: This is approximately $0.6897$, close to $\cos(46^\circ) \approx 0.6947$, so this is a good approximate ratio. - $\frac{29}{20}$: This is greater than 1, so it cannot represent a cosine value. - $\sin(46^\circ)$: This equals $\cos(44^\circ)$, not $\cos(46^\circ)$, so incorrect. - $\cos(136^\circ)$: This is negative and not equal to $\cos(46^\circ)$. 6. **Final answer:** The two correct choices representing $\cos(46^\circ)$ are: - $\sin(44^\circ)$ - $\frac{20}{29}$