1. **State the problem:** We need to find the width $x$ of the soccer field given two sides of a triangle formed by the players' path: one side is 70 m, the other is 112 m, and the angle between them is 104°. 2. **Identify the triangle and formula:** The players' path forms a triangle with sides 70 m and 112 m enclosing an angle of 104°. We can use the Law of Cosines to find the third side $x$ (the width of the field). The Law of Cosines states: $$x^2 = a^2 + b^2 - 2ab \cos(C)$$ where $a=70$, $b=112$, and $C=104^\circ$. 3. **Apply the formula:** $$x^2 = 70^2 + 112^2 - 2 \times 70 \times 112 \times \cos(104^\circ)$$ 4. **Calculate each term:** $$70^2 = 4900$$ $$112^2 = 12544$$ 5. **Calculate the cosine term:** $$\cos(104^\circ) \approx -0.2419$$ 6. **Substitute values:** $$x^2 = 4900 + 12544 - 2 \times 70 \times 112 \times (-0.2419)$$ 7. **Simplify multiplication:** $$2 \times 70 \times 112 = 15680$$ 8. **Calculate the product with cosine:** $$15680 \times (-0.2419) = -3794.59$$ 9. **Substitute back:** $$x^2 = 4900 + 12544 - (-3794.59) = 4900 + 12544 + 3794.59$$ 10. **Sum the terms:** $$x^2 = 21238.59$$ 11. **Find $x$ by taking the square root:** $$x = \sqrt{21238.59} \approx 145.7$$ **Final answer:** The width $x$ of the soccer field is approximately **145.7 meters**.