1. **State the problem:** We are given two legs of a right triangle, $a=3$ miles and $b=2.8$ miles, and we want to find the length of the hypotenuse $c$ using the Pythagorean theorem. 2. **Formula:** The Pythagorean theorem states: $$c^2 = a^2 + b^2$$ This applies only to right triangles, where $c$ is the side opposite the right angle. 3. **Substitute the values:** $$c^2 = 3^2 + 2.8^2$$ 4. **Calculate squares:** $$c^2 = 9 + 7.84$$ 5. **Add the squares:** $$c^2 = 16.84$$ 6. **Take the square root of both sides:** $$c = \sqrt{16.84}$$ 7. **Calculate the square root:** $$c \approx 4.1037$$ 8. **Interpretation:** The hypotenuse $c$ is approximately 4.1 miles. 9. **Additional problem:** Find $c$ if $a=840$ and $b=1345$. 10. **Apply the formula:** $$c^2 = 840^2 + 1345^2$$ 11. **Calculate squares:** $$c^2 = 705600 + 1809025$$ 12. **Add the squares:** $$c^2 = 2514625$$ 13. **Take the square root:** $$c = \sqrt{2514625}$$ 14. **Calculate the square root:** $$c \approx 1585.77$$ 15. **Interpretation:** The hypotenuse $c$ is approximately 1585.77 units (miles or other units depending on context).