1. The problem asks to identify which law or theorem is described by the formulas: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \quad \text{and} \quad \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$$ 2. These formulas relate the sides of a triangle to the sines of their opposite angles. 3. The Pythagorean Theorem relates the squares of the sides in a right triangle, not ratios involving sines. 4. The Cosine Law relates the lengths of sides to the cosine of an angle, not sine. 5. The Tangent Law involves tangents of half-angles, not sine ratios. 6. The Sine Law states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ 7. Equivalently, the reciprocal form: $$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$$ 8. Therefore, the formulas given describe the Sine Law. **Final answer:** d) Sine Law