1. The problem is to find the length $f$ in a right-angled triangle where the angle adjacent to $f$ is $56^\circ$ and the hypotenuse is $5.7$ cm. 2. Use the cosine formula: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. Substitute the known values: $$\cos(56^\circ) = \frac{f}{5.7}$$ 4. Solve for $f$: $$f = 5.7 \times \cos(56^\circ)$$ 5. Calculate $f$ using a calculator: $$f \approx 5.7 \times 0.5592 = 3.2$$ 6. The length $f$ to 1 decimal place is $3.2$ cm.