1. **State the problem:** We want to find the height of the cliff using the given triangle with angles and side lengths. 2. **Given data:** - Angle at C: $72^\circ$ - Angle at B: $58^\circ$ - Side BA (opposite angle C): $18.4$ m 3. **Find angle A:** $$ A = 180^\circ - 72^\circ - 58^\circ = 50^\circ $$ 4. **Use the Law of Sines:** $$ \frac{BC}{\sin A} = \frac{BA}{\sin C} $$ 5. **Substitute known values:** $$ \frac{BC}{\sin 50^\circ} = \frac{18.4}{\sin 72^\circ} $$ 6. **Solve for BC:** $$ BC = \frac{18.4 \times \sin 50^\circ}{\sin 72^\circ} $$ Calculate intermediate values: $$ \sin 50^\circ \approx 0.7660, \quad \sin 72^\circ \approx 0.9511 $$ $$ BC = \frac{18.4 \times 0.7660}{0.9511} \approx \frac{14.0944}{0.9511} \approx 14.82 \text{ m} $$ 7. **Find the height (altitude) using angle B:** Height $h = BC \times \sin 58^\circ$ $$ \sin 58^\circ \approx 0.8480 $$ $$ h = 14.82 \times 0.8480 \approx 12.57 \text{ m} $$ 8. **Conclusion:** The height of the cliff is approximately $12.6$ meters, not $17.7$ meters. **Explanation:** Your approach was mostly correct in using the Law of Sines and sine functions, but the angle values and side used for BC calculation were slightly off, leading to a different height. Make sure to correctly identify all angles and sides before applying the Law of Sines.