1. **State the problem:** We are given a triangle with sides $a=14$, $c=8$, and angle $B=64^\circ$. We need to find side $b$ using the Law of Cosines. 2. **Formula:** The Law of Cosines states: $$b^2 = a^2 + c^2 - 2ac \cos B$$ This formula relates the lengths of the sides of a triangle to the cosine of one of its angles. 3. **Substitute the known values:** $$b^2 = 14^2 + 8^2 - 2 \times 14 \times 8 \times \cos 64^\circ$$ 4. **Calculate each term:** $$14^2 = 196$$ $$8^2 = 64$$ $$2 \times 14 \times 8 = 224$$ 5. **Evaluate cosine:** $$\cos 64^\circ \approx 0.4384$$ 6. **Plug in and simplify:** $$b^2 = 196 + 64 - 224 \times 0.4384$$ $$b^2 = 260 - 98.1216$$ $$b^2 = 161.8784$$ 7. **Find $b$ by taking the square root:** $$b = \sqrt{161.8784} \approx 12.72$$ **Final answer:** $$b \approx 12.72$$ This means the length of side $b$ is approximately 12.72 units.