1. **Problem:** Find the height of the cliff using the given triangle measurements. 2. **Given:** - Side BC = 18.4 m - Angle A = 50° - Angle C = 58° - Angle B = 72° (since angles in triangle sum to 180°) 3. **Formula:** Use the Law of Sines: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ 4. **Step 1:** Calculate side BC using Law of Sines: $$BC = \frac{18.4 \times \sin 50^\circ}{\sin 58^\circ} = \frac{18.4 \times 0.7660}{0.8480}$$ 5. **Step 2:** Simplify the fraction: $$BC = \frac{\cancel{18.4} \times 0.7660}{\cancel{0.8480}} = 16.62 \text{ m}$$ 6. **Step 3:** Calculate height CD using: $$CD = BC \times \sin 72^\circ = 16.62 \times 0.9511 = 15.8 \text{ m}$$ 7. **Answer:** The height of the cliff is approximately **15.8 m**. 8. **Verification:** The calculations and steps are correct based on the Law of Sines and trigonometric values. --- **Summary:** The solution provided is right and the height of the cliff is 15.8 m to the nearest tenth.