What is the law of cosines and how is it used?

What is the law of cosines and how is it used?

The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It's used to find a side or angle in any triangle.

Can you give me the formula for the law of cosines?

Sure! The formula is: c² = a² + b² - 2ab * cos(C), where c is the side opposite angle C.

How do I apply this formula in a real problem?

Let's say you have a triangle with sides a = 5, b = 7, and you want to find angle C. You would rearrange the formula to solve for cos(C) and then use the inverse cosine function.

What if I only know two sides and the included angle?

In that case, you can still use the law of cosines! You would use the formula to find the length of the third side.

Can you show me an example with numbers?

Absolutely! If a = 5, b = 7, and angle C = 60 degrees, you would calculate c using the formula: c² = 5² + 7² - 257*cos(60°). Let me calculate that for you.