Law of Sines Practice

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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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

When can the Law of Sines be used?

Back

The Law of Sines can be used to solve for unknown sides or angles in a triangle 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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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the formula for finding 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)ab sin(C), where a and b are the lengths of two sides and C is the included angle.

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CCSS.HSG.SRT.D.9

Front

If A=65°, C=65°, and a=12, what is B?

Back

B = 50°.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

If A=65°, C=65°, and a=12, what is b?

Back

b = 10.1.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

If A=65°, C=65°, and a=12, what is c?

Back

c = 12.

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CCSS.HSG.SRT.D.10

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 a side length to the sine of its opposite angle is the same for all three sides and angles in the triangle.

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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 relation to the Law of Sines?

Back

The Law of Cosines is used when the Law of Sines cannot be applied, particularly in cases where you have two sides and the included angle (SAS) or all three sides (SSS).

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

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

What is the Law of Sines used for in real-world applications?

Back

The Law of Sines is used in various fields such as navigation, architecture, and engineering to solve problems involving triangles.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11