1. **State the problem:** Marla's garden is divided into two sections, zucchini and squash, forming a right triangle with a base of 4 m. The dividing line creates angles of 26° in the zucchini patch and 18° in the squash section. We need to find the area of the zucchini patch. 2. **Identify the triangle and angles:** The base is 4 m, and the two angles adjacent to the base are 26° (zucchini) and 18° (squash). Since the garden base and shed form a 90° angle, the total angle at the base is 90°, and the dividing line splits this into 26° and 18° angles. 3. **Calculate the length of the dividing line (height) using trigonometry:** The dividing line is the height from the base to the shed, which can be found by considering the right triangle formed. 4. **Use the tangent function for the 26° angle in the zucchini patch:** $$\tan(26^\circ) = \frac{h}{x}$$ where $h$ is the height (dividing line length) and $x$ is the horizontal segment adjacent to the 26° angle. 5. **Use the tangent function for the 18° angle in the squash section:** $$\tan(18^\circ) = \frac{h}{4 - x}$$ 6. **Set up the system of equations:** $$h = x \tan(26^\circ)$$ $$h = (4 - x) \tan(18^\circ)$$ 7. **Equate the two expressions for $h$ and solve for $x$:** $$x \tan(26^\circ) = (4 - x) \tan(18^\circ)$$ $$x \tan(26^\circ) = 4 \tan(18^\circ) - x \tan(18^\circ)$$ $$x \tan(26^\circ) + x \tan(18^\circ) = 4 \tan(18^\circ)$$ $$x (\tan(26^\circ) + \tan(18^\circ)) = 4 \tan(18^\circ)$$ $$x = \frac{4 \tan(18^\circ)}{\tan(26^\circ) + \tan(18^\circ)}$$ 8. **Calculate $x$ numerically:** $$\tan(26^\circ) \approx 0.4877$$ $$\tan(18^\circ) \approx 0.3249$$ $$x = \frac{4 \times 0.3249}{0.4877 + 0.3249} = \frac{1.2996}{0.8126} \approx 1.6$$ 9. **Calculate $h$ using $x$:** $$h = x \tan(26^\circ) = 1.6 \times 0.4877 \approx 0.78$$ 10. **Calculate the area of the zucchini patch:** The zucchini patch is a triangle with base $x = 1.6$ m and height $h = 0.78$ m. $$\text{Area} = \frac{1}{2} \times x \times h = \frac{1}{2} \times 1.6 \times 0.78 = 0.624$$ **Final answer:** The area of the zucchini patch is approximately **0.624 square meters**.