1. **State the problem:** Solve the equation $$\frac{8}{f} = \cos 46^\circ$$ for $f$ and give the answer to 2 decimal places. 2. **Recall the formula and rules:** The equation relates $f$ and the cosine of an angle. To isolate $f$, multiply both sides by $f$ and then divide both sides by $\cos 46^\circ$. 3. **Isolate $f$:** $$\frac{8}{f} = \cos 46^\circ \implies 8 = f \cdot \cos 46^\circ \implies f = \frac{8}{\cos 46^\circ}$$ 4. **Calculate $\cos 46^\circ$:** Using a calculator, $\cos 46^\circ \approx 0.6946583705$ 5. **Evaluate $f$:** $$f = \frac{8}{0.6946583705} \approx 11.516$$ 6. **Round to 2 decimal places:** $$f \approx 11.52$$ **Final answer:** $f = 11.52$