1. **State the problem:** We need to find the length $f$ in a right triangle where one angle is $38^\circ$, the adjacent side to this angle is $7.2$ cm, and $f$ is the side opposite the $38^\circ$ angle. 2. **Identify the sides and trigonometric function:** The side adjacent to the angle is $7.2$ cm, and the side opposite the angle is $f$. We can use the tangent function, which relates opposite and adjacent sides: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Write the formula for $f$:** $$\tan(38^\circ) = \frac{f}{7.2} \implies f = 7.2 \times \tan(38^\circ)$$ 4. **Calculate $\tan(38^\circ)$:** Using a calculator, $\tan(38^\circ) \approx 0.7813$ 5. **Calculate $f$:** $$f = 7.2 \times 0.7813 = 5.6249$$ 6. **Round to 1 decimal place:** $$f \approx 5.6$$ cm **Final answer:** $f = 5.6$ cm