1. The problem asks whether the primary trigonometric ratios can be used in non-right triangles. 2. The primary trigonometric ratios (sine, cosine, tangent) are defined based on right triangles, relating angles to side lengths. 3. For non-right triangles, these ratios do not directly apply unless the triangle is split into right triangles or other methods like the Law of Cosines or Law of Sines are used. 4. Therefore, the correct answer is c) It depends, because sometimes you can use trigonometric ratios if you create right triangles within the non-right triangle. 5. The second problem involves verifying the student's formula for cos \theta in a triangle with sides 12, 8, and 11, where \theta is opposite the side of length 11. 6. The Law of Cosines states: $$\cos \theta = \frac{a^2 + b^2 - c^2}{2ab}$$ where \theta is the angle opposite side \textit{c}. 7. Here, \theta is opposite side 11, so: $$\cos \theta = \frac{12^2 + 8^2 - 11^2}{2 \times 12 \times 8}$$ 8. The student's formula matches the Law of Cosines exactly. 9. Therefore, the student is correct, answer a) Yes. Final answers: 21. c) It depends 22. a) Yes