1. **State the problem:** We need to find which two expressions represent $\cos(76^\circ)$ based on the given right triangle with hypotenuse 130 and adjacent side 32 to the $76^\circ$ angle. 2. **Recall the cosine definition:** $$\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$$ For $\theta = 76^\circ$, $$\cos(76^\circ) = \frac{32}{130}$$ 3. **Simplify the fraction:** $$\frac{32}{130} = \frac{\cancel{2} \times 16}{\cancel{2} \times 65} = \frac{16}{65}$$ 4. **Check the given choices:** - $\cos(166^\circ)$: Since $\cos(180^\circ - x) = -\cos(x)$, $\cos(166^\circ) = -\cos(14^\circ)$, which is not equal to $\cos(76^\circ)$. - $\frac{65}{16}$: This is the reciprocal of $\frac{16}{65}$, so it does not equal $\cos(76^\circ)$. - $\sin(76^\circ)$: Using the complementary angle identity, $\sin(76^\circ) = \cos(14^\circ)$, which is not equal to $\cos(76^\circ)$. - $\frac{16}{65}$: This matches the simplified ratio of adjacent over hypotenuse, so it represents $\cos(76^\circ)$. - $\sin(14^\circ)$: Since $\sin(14^\circ) = \cos(76^\circ)$ (complementary angles), this also represents $\cos(76^\circ)$. 5. **Final answer:** The two expressions representing $\cos(76^\circ)$ are: $$\frac{16}{65} \quad \text{and} \quad \sin(14^\circ)$$