1. **State the problem:** We have a right-angled triangle with a hypotenuse of length 27.9 cm and an angle of 53° adjacent to the side of length $n$. We need to find the length $n$ using the cosine of 53°. 2. **Recall the cosine definition:** In a right triangle, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$. 3. **Identify sides:** Here, the side adjacent to the 53° angle is $n$, and the hypotenuse is 27.9 cm. 4. **Write the equation:** $$\cos 53^\circ = \frac{n}{27.9}$$ 5. **Solve for $n$:** $$n = 27.9 \times \cos 53^\circ$$ 6. **Calculate $\cos 53^\circ$:** $$\cos 53^\circ \approx 0.6018$$ 7. **Find $n$:** $$n = 27.9 \times 0.6018 = 16.79$$ 8. **Round to 2 decimal places:** $$n = 16.79$$ cm **Final answer:** The length $n$ is approximately 16.79 cm.