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. It is expressed as: 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. 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).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

When do you use the Law of Sines?

Back

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).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

When do you use the Law of Cosines?

Back

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

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the formula for the area of a triangle using the Law of Sines?

Back

The area (A) of a triangle can be calculated using the formula: A = (1/2) * a * b * sin(C), where a and b are two sides and C is the included angle.

Tags

CCSS.HSG.SRT.D.9

Front

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

Back

To find an angle using the Law of Sines, rearrange the formula: sin(A)/a = sin(B)/b to solve for the angle: A = sin^(-1)(b * sin(A)/a).

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

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

What is the significance of the Law of Sines in solving triangles?

Back

The Law of Sines allows for the calculation of unknown angles and sides in non-right triangles, making it essential for solving various triangle problems.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the significance of the Law of Cosines in solving triangles?

Back

The Law of Cosines is crucial for solving triangles when the Law of Sines cannot be applied, particularly in cases involving the lengths of all three sides.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

How do you apply the Law of Cosines to find a side?

Back

To find a side using the Law of Cosines, use the formula: c = √(a² + b² - 2ab*cos(C)), where a and b are the known sides and C is the included angle.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11