1. **Problem Statement:** We have a triangle with points A, B, and C. Points A and B are opposite sides of the Grand Canyon. Point C is 200 yards from A. Angle at B is 87 degrees and angle at C is 67 degrees. We need to find the distance between A and B. 2. **Known values:** - $AC = 200$ yards - $\angle B = 87^\circ$ - $\angle C = 67^\circ$ 3. **Find:** $AB$ (distance between A and B) 4. **Step 1: Find the missing angle $\angle A$** Using the triangle angle sum rule: $$\angle A = 180^\circ - \angle B - \angle C = 180^\circ - 87^\circ - 67^\circ = 26^\circ$$ 5. **Step 2: Use the Law of Sines** The Law of Sines states: $$\frac{AB}{\sin C} = \frac{AC}{\sin B} = \frac{BC}{\sin A}$$ We want $AB$, so: $$AB = \frac{AC \times \sin C}{\sin B}$$ 6. **Step 3: Substitute known values** $$AB = \frac{200 \times \sin 67^\circ}{\sin 87^\circ}$$ 7. **Step 4: Calculate sines and evaluate** - $\sin 67^\circ \approx 0.9205$ - $\sin 87^\circ \approx 0.9986$ So, $$AB = \frac{200 \times 0.9205}{0.9986} \approx \frac{184.1}{0.9986} \approx 184.35$$ 8. **Final answer:** The distance between points A and B is approximately **184.35 yards**. This completes the solution using the Law of Sines.