1. **State the problem:** We are given a triangle with vertices Miami, Bermuda, and San Juan. The side between Miami and Bermuda is 965 miles, the side between Miami and San Juan is 1038 miles, and the angle at Miami is 53 degrees. The question asks for the distance from Bermuda to San Juan. 2. **Identify the known values:** - Side $a = 965$ miles (Miami to Bermuda) - Side $b = 1038$ miles (Miami to San Juan) - Angle $C = 53^\circ$ at Miami 3. **Use the Law of Cosines to find the unknown side $c$ (Bermuda to San Juan):** $$c^2 = a^2 + b^2 - 2ab \cos C$$ 4. **Substitute the known values:** $$c^2 = 965^2 + 1038^2 - 2 \times 965 \times 1038 \times \cos 53^\circ$$ 5. **Calculate each term:** $$965^2 = 931225$$ $$1038^2 = 1077444$$ $$2 \times 965 \times 1038 = 2003340$$ $$\cos 53^\circ \approx 0.6018$$ 6. **Calculate the product:** $$2003340 \times 0.6018 \approx 1206220.61$$ 7. **Calculate $c^2$:** $$c^2 = 931225 + 1077444 - 1206220.61 = 803448.39$$ 8. **Find $c$ by taking the square root:** $$c = \sqrt{803448.39} \approx 896.36$$ 9. **Conclusion:** The distance from Bermuda to San Juan is approximately 896 miles.