Law of Sines & Cosines Check

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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. Formula: a/sin(A) = b/sin(B) = c/sin(C).

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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 or angle in a triangle when you know two sides and the included angle or all three sides. Formula: c² = a² + b² - 2ab*cos(C).

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When do you use the Law of Sines?

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

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When do you use the Law of Cosines?

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

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What criteria can be used with the Law of Sines?

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The criteria for the Law of Sines are SSA, ASA, and AAS.

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What criteria can be used with the Law of Cosines?

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The criteria for the Law of Cosines are SSS and SAS.

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If you know two sides and the included angle, which law do you use?

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You would use the Law of Cosines.

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If you know two angles and one side, which law do you use?

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You would use the Law of Sines.

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What is the formula for the Law of Sines?

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The formula is a/sin(A) = b/sin(B) = c/sin(C).

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What is the formula for the Law of Cosines?

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The formula is c² = a² + b² - 2ab*cos(C).