Law of Sines & Cosines

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.

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What are the criteria for using the Law of Sines?

Back

The criteria for using the Law of Sines are SSA (Side-Side-Angle), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side).

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, and is used to find a side or angle in a triangle.

Front

What are the criteria for using the Law of Cosines?

Back

The criteria for using the Law of Cosines are SSS (Side-Side-Side) and SAS (Side-Angle-Side).

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When would you use the Law of Sines?

Back

You would use the Law of Sines when you have two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Front

When would you use the Law of Cosines?

Back

You would use the Law of Cosines when you have two sides and the included angle (SAS) or all three sides (SSS).

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What is the formula for the Law of Sines?

Back

The formula for the Law of Sines is: (a/sin(A)) = (b/sin(B)) = (c/sin(C)), where a, b, and c are the sides of the triangle and A, B, and C are the opposite angles.

Front

What is the formula for the Law of Cosines?

Back

The formula for the Law of Cosines is: c² = a² + b² - 2ab * cos(C), where a and b are the lengths of two sides, C is the included angle, and c is the length of the side opposite angle C.

Front

What does SSA stand for in triangle criteria?

Back

SSA stands for Side-Side-Angle, a criterion used for the Law of Sines.

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What does ASA stand for in triangle criteria?

Back

ASA stands for Angle-Side-Angle, a criterion used for the Law of Sines.