1. **State the problem:** We have a right triangle with hypotenuse length 20 and a leg opposite the missing angle measuring 13. We need to find the measure of the missing angle. 2. **Formula used:** To find an angle when we know the opposite side and hypotenuse, we use the sine function: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply the formula:** $$\sin(\theta) = \frac{13}{20}$$ 4. **Calculate the sine value:** $$\sin(\theta) = 0.65$$ 5. **Find the angle:** Use the inverse sine (arcsin) function: $$\theta = \sin^{-1}(0.65)$$ 6. **Use a calculator:** $$\theta \approx 40.54^\circ$$ 7. **Round to the nearest tenth:** $$\theta \approx 40.5^\circ$$ **Final answer:** The missing angle is approximately **40.5 degrees**.