Law of Sines and 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. It is 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 useful for finding a side when two sides and the included angle are known. It is expressed as: c² = a² + b² - 2ab*cos(C).

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When should 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 should you use the Law of Cosines?

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

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

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To find the length of a side using the Law of Cosines, rearrange the formula: c = √(a² + b² - 2ab*cos(C)).

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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).

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What is the relationship between the angles and sides in a triangle according to the Law of Sines?

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The Law of Sines shows that the ratio of each side to the sine of its opposite angle is equal, indicating a proportional relationship.

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If angle A = 30° and side a = 10, how do you find side b using the Law of Sines?

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Using the Law of Sines: b = (a * sin(B)) / sin(A). You need to know angle B to calculate side b.

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What is the significance of the Law of Cosines in triangle calculations?

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The Law of Cosines is significant because it allows for the calculation of unknown sides or angles in triangles that are not right-angled.

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How do you apply the Law of Sines to find an unknown angle?

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To find an unknown angle using the Law of Sines, rearrange the formula: sin(A) = a * sin(B) / b, then use the inverse sine function.