Law of Sine and Cosine
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Law of Sines?
Back
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides and angles in the triangle. It is expressed as: a/sin(A) = b/sin(B) = c/sin(C).
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
2.
FLASHCARD QUESTION
Front
What is 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. It is useful for finding a side when two sides and the included angle are known. It is expressed as: c² = a² + b² - 2ab*cos(C).
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
3.
FLASHCARD QUESTION
Front
When do you use the Law of Sines?
Back
The Law of Sines is used when you have either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA) in a triangle.
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
4.
FLASHCARD QUESTION
Front
When do you use the Law of Cosines?
Back
The Law of Cosines is used when you have two sides and the included angle (SAS) or all three sides (SSS) of a triangle.
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
5.
FLASHCARD QUESTION
Front
Find the length of side AC if AB = 10, BC = 12, and angle A = 60 degrees.
Back
AC = 14 (using the Law of Cosines).
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
6.
FLASHCARD QUESTION
Front
Find the distance a pilot travels if he must redirect from Norfolk to Raleigh, given the distances to Richmond and Raleigh are 143 miles and 160 miles respectively, and the angle between these paths is 45 degrees.
Back
Distance = 151 miles (using the Law of Cosines).
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
7.
FLASHCARD QUESTION
Front
What is the formula for the Law of Sines?
Back
The formula is: a/sin(A) = b/sin(B) = c/sin(C).
Tags
CCSS.HSG.SRT.D.10
CCSS.HSG.SRT.D.11
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