1. **State the problem:** We have a right triangle formed by the central pole (20 ft), the slant height (26 ft), and the base of the tent. We want to find the angle between the central pole and the slant height. 2. **Identify the sides:** The central pole is one leg of the right triangle (20 ft), the slant height is the hypotenuse (26 ft), and the base is the other leg. 3. **Use the sine function:** The sine of the angle between the pole and the slant height is the ratio of the opposite side (pole) to the hypotenuse (slant height): $$\sin(\theta) = \frac{20}{26}$$ 4. **Calculate the sine value:** $$\sin(\theta) = \frac{20}{26} = \frac{10}{13} \approx 0.7692$$ 5. **Find the angle using arcsine:** $$\theta = \arcsin\left(\frac{10}{13}\right) \approx 50.28^\circ$$ 6. **Interpretation:** The angle the tent pole makes with the slant height is approximately $50.28^\circ$. **Final answer:** The sine of the missing angle is $\frac{20}{26}$, and the angle is approximately $50.28^\circ$.