1. **State the problem:** Find the volume of a right triangular prism where the base is a right triangle with one leg 5.7 cm, an adjacent angle of 42°, and the prism height (length) is 8 cm. 2. **Formula for volume of a prism:** $$\text{Volume} = \text{Base Area} \times \text{Height}$$ 3. **Find the base area:** The base is a right triangle. One leg is 5.7 cm, and the other leg can be found using the angle 42° adjacent to the 5.7 cm side. 4. Use trigonometry to find the other leg: $$\text{Other leg} = 5.7 \times \tan(42^\circ)$$ 5. Calculate the other leg: $$5.7 \times \tan(42^\circ) \approx 5.7 \times 0.9004 = 5.1323 \text{ cm}$$ 6. Calculate the base area of the right triangle: $$\text{Area} = \frac{1}{2} \times 5.7 \times 5.1323 \approx \frac{1}{2} \times 29.256 = 14.628 \text{ cm}^2$$ 7. Calculate the volume of the prism: $$\text{Volume} = 14.628 \times 8 = 117.024 \text{ cm}^3$$ **Final answer:** The volume of the prism is approximately **117.0 cm³**.