1. **State the problem:** We have a right triangle with a right angle at the bottom-left corner, an angle of 39° at the top-left corner, the horizontal leg adjacent to the 39° angle is 5 ft, and the vertical leg opposite the 39° angle is $x$. We need to find $x$ rounded to the nearest hundredth. 2. **Formula and rules:** In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, $\theta = 39^\circ$, opposite side = $x$, adjacent side = 5. 3. **Set up the equation:** $$\tan(39^\circ) = \frac{x}{5}$$ 4. **Solve for $x$:** Multiply both sides by 5: $$5 \times \tan(39^\circ) = x$$ 5. **Calculate the value:** Using a calculator, $$\tan(39^\circ) \approx 0.80978$$ So, $$x = 5 \times 0.80978 = 4.0489$$ 6. **Round the answer:** Rounded to the nearest hundredth, $$x \approx 4.05$$ **Final answer:** $$x = 4.05 \text{ ft}$$