1. The problem asks to identify which formula set corresponds to a given set of trigonometric formulas. 2. The formulas given are: $$c^2 = a^2 + b^2 - 2ab \cos C$$ $$\cos C = \frac{a^2 + b^2 - c^2}{2ab}$$ $$a^2 = b^2 + c^2 - 2bc \cos A$$ $$\cos A = \frac{b^2 + c^2 - a^2}{2bc}$$ $$b^2 = a^2 + c^2 - 2ac \cos B$$ $$\cos B = \frac{a^2 + c^2 - b^2}{2ac}$$ 3. These formulas are the Law of Cosines, which relate the lengths of sides of a triangle to the cosine of one of its angles. 4. The Pythagorean Theorem is a special case of the Law of Cosines when the angle is 90 degrees, but the formulas here include the cosine term explicitly. 5. Therefore, the correct answer for question 17 is (b) Cosine Law. 6. For question 18, the problem describes a triangle with an angle of 32°, a side opposite that angle of length 7.0, an adjacent side of length 9.0, and an unknown side $x$ opposite an unlabeled angle. 7. To find side $x$, we need to use a trigonometric tool that relates two sides and the included angle or two sides and an opposite angle. 8. The Pythagorean Theorem applies only to right triangles and requires a right angle, which is not specified here. 9. The Sine Law relates ratios of sides to sines of opposite angles but requires knowing an angle-side opposite pair. 10. The Cosine Law relates sides and the cosine of the included angle and is useful when two sides and the included angle are known. 11. Since we have two sides and the included angle (32°), the best tool is the Cosine Law. 12. Therefore, the answer for question 18 is (d) The Cosine Law.