Final answer:
Use the Law of Cosines when you are given 3 sides and an angle, as it applies to all types of triangles. Law of Sines applies to any triangle but is often used when an angle opposite a given side is known.
Step-by-step explanation:
If you are given 3 sides and an angle of a triangle, the correct approach to finding unknown angles or sides depends on the information you have. If the angle is between two known sides, you should use the Law of Cosines, as it works for all types of triangles including acute, obtuse, and right-angled triangles. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. Conversely, the Law of Sines relates the lengths of sides to the sines of the angles and applies to any triangle, not just right-angled ones. Therefore, the correct answer is (a) Law of Cosines; it works for all types of triangles.
For example, given triangle sides a, b, c, and angle γ between sides a and b, you can determine side c using the Law of Cosines formula: c² = a² + b² - 2ab cos γ. The Law of Cosines is particularly useful when you cannot directly apply the Law of Sines, such as when an angle opposite a given side is not known.
Trigonometry is reliable because it is based on a set of postulates that dictate the relationships between the angles and sides of triangles. Predictions based on trigonometric laws must agree, just as principles of physics must describe nature accurately and be verified by experiment.