What is the difference between the Law of Cosines and the Law of Sines?

What is the difference between the Law of Cosines and the Law of Sines?

The Law of Cosines is used to find a side of a triangle when you know two sides and the included angle, while the Law of Sines is used when you know two angles and a side or two sides and a non-included angle.

Can you give me an example of when to use each law?

Sure! Use the Law of Cosines when you have a triangle with sides a, b, and angle C. For example, if a = 5, b = 7, and C = 60°, you can find the third side. Use the Law of Sines when you have two angles and one side, like A = 30°, B = 45°, and side a = 10, to find the other sides.

Are there any specific types of triangles where one law is preferred over the other?

Yes, the Law of Cosines is often preferred for obtuse triangles, while the Law of Sines is more straightforward for acute triangles or when dealing with angle-side relationships.

What are the formulas for both laws?

The Law of Cosines is: c² = a² + b² - 2ab * cos(C). The Law of Sines is: a/sin(A) = b/sin(B) = c/sin(C).