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 the angle opposite that side 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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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

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. Formula: c² = a² + b² - 2ab*cos(C).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

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

Back

To find a side length using the Law of Sines, use the formula: a/sin(A) = b/sin(B). Rearrange to find the unknown side.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

How do you find an angle using the Law of Cosines?

Back

To find an angle using the Law of Cosines, rearrange the formula: cos(C) = (a² + b² - c²) / (2ab).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

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).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the formula for the Law of Cosines?

Back

The formula for the Law of Cosines is: c² = a² + b² - 2ab*cos(C).

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

If m

Back

To find m

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CCSS.8.G.A.5

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.

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CCSS.HSG.CO.C.10

Front

How do you calculate the area of a triangle using the Law of Sines?

Back

Area = (1/2) * a * b * sin(C), where a and b are two sides and C is the included angle.

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CCSS.HSG.SRT.D.9

Front

What is the significance of the included angle in the Law of Cosines?

Back

The included angle is the angle between the two sides used in the Law of Cosines formula, which is essential for calculating the third side.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11