1. **State the problem:** We are given a triangle with sides |CF| = 22 cm, |EF| = 11.8 cm, and the included angle $\angle EFC = 110^\circ$. We need to find the length |CE| using the cosine rule. 2. **Recall the cosine rule:** For any triangle with sides $a$, $b$, and $c$, and angle $\theta$ opposite side $c$, the cosine rule states: $$c^2 = a^2 + b^2 - 2ab \cos(\theta)$$ 3. **Assign values:** Here, let: - $a = |CF| = 22$ cm - $b = |EF| = 11.8$ cm - $\theta = 110^\circ$ - $c = |CE|$ (unknown side) 4. **Apply the cosine rule:** $$|CE|^2 = 22^2 + 11.8^2 - 2 \times 22 \times 11.8 \times \cos(110^\circ)$$ 5. **Calculate each term:** $$22^2 = 484$$ $$11.8^2 = 139.24$$ 6. **Calculate the cosine term:** $$\cos(110^\circ) = \cos(180^\circ - 70^\circ) = -\cos(70^\circ) \approx -0.3420$$ 7. **Substitute and simplify:** $$|CE|^2 = 484 + 139.24 - 2 \times 22 \times 11.8 \times (-0.3420)$$ $$= 484 + 139.24 + 177.43$$ $$= 800.67$$ 8. **Find |CE| by taking the square root:** $$|CE| = \sqrt{800.67} \approx 28.3 \text{ cm}$$ **Final answer:** $$|CE| \approx 28.3 \text{ cm}$$