1. **Problem:** Find the length |BE| to 1 decimal place. 2. **Given:** The diagram shows points B, E, and other points with distances 3.1 m, 5.4 m, 9.2 m, and 10.67 m. 3. **Approach:** Use the Pythagorean theorem or distance formula depending on the coordinates or triangle formed. 4. Since the problem is incomplete without coordinates or clear triangle sides, assume triangle BEC with sides 9.2 m and 5.4 m adjacent to E and C. 5. Calculate |BE| using Pythagoras: $$|BE|=\sqrt{(10.67)^2 - (9.2)^2}$$ 6. Calculate intermediate values: $$10.67^2=113.8489$$ $$9.2^2=84.64$$ 7. Subtract: $$113.8489 - 84.64 = 29.2089$$ 8. Take square root: $$|BE|=\sqrt{29.2089} = 5.4$$ 9. **Answer:** |BE| = 5.4 m (to 1 decimal place). --- 1. **Problem:** Find the angle ∠CEB to 1 decimal place. 2. **Given:** Triangle CEB with sides known or calculated. 3. Use cosine rule: $$\cos(\angle CEB) = \frac{|CE|^2 + |EB|^2 - |CB|^2}{2 \times |CE| \times |EB|}$$ 4. Substitute values (assuming |CE|=5.4 m, |EB|=5.4 m, |CB|=3.1 m): $$\cos(\angle CEB) = \frac{5.4^2 + 5.4^2 - 3.1^2}{2 \times 5.4 \times 5.4}$$ 5. Calculate squares: $$5.4^2=29.16$$ $$3.1^2=9.61$$ 6. Substitute: $$\cos(\angle CEB) = \frac{29.16 + 29.16 - 9.61}{2 \times 5.4 \times 5.4} = \frac{48.71}{58.32} = 0.8353$$ 7. Calculate angle: $$\angle CEB = \cos^{-1}(0.8353) = 33.3^\circ$$ 8. **Answer:** ∠CEB = 33.3° (to 1 decimal place).