1. **State the problem:** We need to find the area of a right triangle where one leg is 13 units and the angle adjacent to this leg is 51°. 2. **Identify the known values:** - One leg (adjacent to the angle) = 13 units - Angle adjacent to this leg = 51° - The triangle is right-angled, so the other angle is 90° and the remaining angle is 39° (since 180° total). 3. **Formula for the area of a right triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 4. **Find the other leg (height):** Since the given side is adjacent to the 51° angle, the other leg opposite to 51° can be found using the tangent function: $$\tan(51^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{\text{height}}{13}$$ 5. **Calculate the height:** $$\text{height} = 13 \times \tan(51^\circ)$$ 6. **Calculate the height value:** $$\tan(51^\circ) \approx 1.2349$$ $$\text{height} = 13 \times 1.2349 = 16.0537$$ 7. **Calculate the area:** $$\text{Area} = \frac{1}{2} \times 13 \times 16.0537$$ 8. **Simplify the area calculation:** $$\text{Area} = \frac{1}{2} \times 13 \times 16.0537 = \frac{\cancel{2} \times 13 \times 16.0537}{\cancel{2}} = 6.5 \times 16.0537$$ 9. **Final area value:** $$\text{Area} = 104.348$$ 10. **Round to the nearest tenth:** $$\text{Area} \approx 104.3$$ square units. **Answer:** The area of the triangle is approximately **104.3** square units.