What is the Law of Cosines?
Law of Cosines

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•
Mathematics
•
11th - 12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
Back
The Law of Cosines states that in any triangle, the square of the length of one side (c) is equal to the sum of the squares of the lengths of the other two sides (a and b) minus twice the product of those two sides multiplied by the cosine of the included angle (C). Formula: c² = a² + b² - 2ab cos(C).
2.
FLASHCARD QUESTION
Front
When should you use the Law of Cosines instead of the Law of Sines?
Back
Use the Law of Cosines when you have two sides and the included angle (SAS) or all three sides (SSS) of a triangle. The Law of Sines is used when you have two angles and one side (ASA or AAS) or two sides and a non-included angle (SSA).
3.
FLASHCARD QUESTION
Front
What is the formula for the Law of Cosines?
Back
The Law of Cosines can be expressed as: c² = a² + b² - 2ab cos(C), a² = b² + c² - 2bc cos(A), b² = a² + c² - 2ac cos(B).
4.
FLASHCARD QUESTION
Front
What does the term 'included angle' mean in the context of the Law of Cosines?
Back
The included angle is the angle formed between two sides of a triangle. In the Law of Cosines, it is the angle opposite the side being calculated.
5.
FLASHCARD QUESTION
Front
How can the Law of Cosines be used to find the length of a side in a triangle?
Back
To find the length of a side using the Law of Cosines, rearrange the formula to isolate the side of interest. For example, to find side c: c = √(a² + b² - 2ab cos(C)).
6.
FLASHCARD QUESTION
Front
What is the relationship between the Law of Cosines and the Pythagorean theorem?
Back
The Law of Cosines generalizes the Pythagorean theorem. When the angle C is 90 degrees, cos(90°) = 0, and the Law of Cosines simplifies to the Pythagorean theorem: c² = a² + b².
7.
FLASHCARD QUESTION
Front
Can the Law of Cosines be used for non-right triangles?
Back
Yes, the Law of Cosines is applicable to all types of triangles, including acute and obtuse triangles.
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