Law of Sines or Cosines

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What is the Law of Sines?

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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 is the Law of Cosines?

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The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is used to find a side or angle in a triangle when the Law of Sines cannot be applied.

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When would you use the Law of Sines?

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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.

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When would you use the Law of Cosines?

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The Law of Cosines is used when you have either two sides and the included angle (SAS) or all three sides (SSS) of a triangle.

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What is the formula for the Law of Sines?

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

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What is the formula for the Law of Cosines?

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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.

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How do you determine which law to use in a triangle problem?

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Determine the given information: use the Law of Sines for AAS, ASA, or SSA cases, and use the Law of Cosines for SAS or SSS cases.

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Can the Law of Sines be used for non-right triangles?

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Yes, the Law of Sines can be used for any triangle, not just right triangles.

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Can the Law of Cosines be used for right triangles?

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Yes, the Law of Cosines can be used for right triangles, but it is often simpler to use the Pythagorean theorem.

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What is an example of using the Law of Sines?

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Given triangle ABC with angles A=30°, B=60°, and side a=10, find side b. Use the Law of Sines: b = (a * sin(B)) / sin(A) = (10 * sin(60°)) / sin(30°) = 17.32.