1. **State the problem:** We have a right triangle with a right angle at the bottom-left, an angle of 39° at the top-left, a horizontal leg of length 5 ft, and a vertical leg of length $x$ ft. We need to find $x$ rounded to the nearest hundredth. 2. **Identify the trigonometric relationship:** The angle 39° is adjacent to the horizontal leg (5 ft) and opposite the vertical leg ($x$). The tangent function relates the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** $$\tan(39^\circ) = \frac{x}{5}$$ 4. **Solve for $x$:** $$x = 5 \times \tan(39^\circ)$$ 5. **Calculate the value:** $$x = 5 \times \tan(39^\circ) \approx 5 \times 0.80978 = 4.0489$$ 6. **Round to the nearest hundredth:** $$x \approx 4.05$$ **Final answer:** $x = 4.05$ ft