Problem 53
Question
Without using symbols, state the Law of Cosines in your own words.
Step-by-Step Solution
Verified Answer
The Law of Cosines states that in any triangle, the square of a side length is equal to the sum of the squares of the other two side lengths, minus twice the product of those two lengths and the cosine of the included angle.
1Step 1: Understanding the Law
The Law of Cosines is a theorem in geometry that describes the relationship between the lengths of the sides of a triangle and the cosine of one of its angles.
2Step 2: Simplifying Law Structure
It states that for any triangle (right, acute, or obtuse), you can determine the length of one side if you know the lengths of the other two sides and the angle between them.
3Step 3: Stating Law Specifics
Specifically, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, minus twice the product of those two lengths and the cosine of the included angle.
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