Law of sines and Cosines

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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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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 or angle in a triangle when the Law of Sines cannot be applied. It is expressed as: c² = a² + b² - 2ab*cos(C).

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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) in a triangle.

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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.

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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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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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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 to isolate the cosine of the angle: cos(C) = (a² + b² - c²) / (2ab). Then use the inverse cosine function.

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Front

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

Back

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

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Front

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

Back

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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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 geometric problems.

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CCSS.HSG.SRT.D.11