Law of Sines & 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 the angle opposite that side is constant for all three sides of the triangle. It can be expressed as: a/sin(A) = b/sin(B) = c/sin(C).

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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 expressed as: c² = a² + b² - 2ab*cos(C).

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When do 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).

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When do 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 Cosines?

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c² = a² + b² - 2ab*cos(C).

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How do you find the length of a side using the Law of Sines?

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To find the length of a side using the Law of Sines, rearrange the formula: a = b*sin(A)/sin(B).

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What is the relationship between the angles and sides in a triangle?

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In a triangle, the larger the angle, the longer the opposite side. This relationship is fundamental in both the Law of Sines and the Law of Cosines.

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What is the sine of an angle in a right triangle?

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In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

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What is the cosine of an angle in a right triangle?

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In a right triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

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How can you determine if a triangle is valid with given sides?

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A triangle is valid if the sum of the lengths of any two sides is greater than the length of the third side (Triangle Inequality Theorem).