Law of Cosines
Flashcard
•
Mathematics
•
11th - 12th Grade
•
Hard
+1
Standards-aligned
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Law of Cosines?
Back
The Law of Cosines states that for any triangle with sides a, b, and c, and angles A, B, and C opposite those sides, the following relationship holds: c² = a² + b² - 2ab * cos(C).
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
2.
FLASHCARD QUESTION
Front
When would you use the Law of Cosines instead of the Law of Sines?
Back
The Law of Cosines is used when you have either SSS (three sides) or SAS (two sides and the included angle) to find unknown angles or sides.
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
3.
FLASHCARD QUESTION
Front
What is the formula for the Law of Cosines?
Back
c² = a² + b² - 2ab * cos(C).
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
4.
FLASHCARD QUESTION
Front
What criteria must be met to use the Law of Cosines?
Back
The criteria for using the Law of Cosines are SSS (three sides known) or SAS (two sides and the included angle known).
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
5.
FLASHCARD QUESTION
Front
Solve for angle C using the Law of Cosines: a=5, b=7, c=10.
Back
C = cos⁻¹((a² + b² - c²) / (2ab)) = cos⁻¹((5² + 7² - 10²) / (2 * 5 * 7)) = 60°.
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
6.
FLASHCARD QUESTION
Front
If a triangle has sides of lengths 8, 15, and 17, what type of triangle is it?
Back
It is a right triangle, as it satisfies the Pythagorean theorem: 8² + 15² = 17².
Tags
CCSS.8.G.B.8
7.
FLASHCARD QUESTION
Front
What is the relationship between the angles and sides in a triangle according to the Law of Cosines?
Back
The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
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