1. **State the problem:** We have two masts of heights 20 m and 12 m. The line joining their tops makes an angle of 35° with the horizontal. We need to find the distance between the bases of the two masts. 2. **Understand the setup:** Let the distance between the two masts be $d$. The difference in height between the tops is $20 - 12 = 8$ m. 3. **Use trigonometry:** The line joining the tops forms a right triangle with the horizontal distance $d$ and vertical difference 8 m. The angle with the horizontal is 35°. 4. **Apply the tangent function:** $$\tan(35^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{8}{d}$$ 5. **Solve for $d$:** $$d = \frac{8}{\tan(35^\circ)}$$ 6. **Calculate the value:** Using $\tan(35^\circ) \approx 0.7002$, $$d \approx \frac{8}{0.7002} \approx 11.42$$ meters. **Final answer:** The distance between the two masts is approximately $11.42$ meters.