Law of Sines and 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. It is expressed as: a/sin(A) = b/sin(B) = c/sin(C).

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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. 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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Front

When should you use the Law of Sines?

Back

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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Front

When should you use the Law of Cosines?

Back

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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Front

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

Back

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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Front

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).

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CCSS.HSG.SRT.D.11

Front

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

Back

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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Front

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

Back

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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Front

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

Back

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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Front

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

Back

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.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11