1. **Problem Statement:** Find the length $d$ of the base of the large right triangle given the height is 12 m, one angle is 35°, and there is a smaller triangle inside with a 10° angle adjacent to the 35° angle. 2. **Understanding the Triangle:** The large triangle is right-angled with height 12 m and base $d$. The angle at the bottom left corner is 35°, so the angle at the bottom right corner is 90°. 3. **Using Trigonometry:** In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 4. **Applying to the Large Triangle:** For the 35° angle, $$\tan(35^\circ) = \frac{12}{d}$$ 5. **Solving for $d$:** Rearranging, $$d = \frac{12}{\tan(35^\circ)}$$ 6. **Calculate $\tan(35^\circ)$:** Using a calculator or table, $$\tan(35^\circ) \approx 0.7002$$ 7. **Final Calculation:** $$d = \frac{12}{0.7002} \approx 17.14$$ **Answer:** The length $d$ is approximately 17.14 meters.