Exploring the Law of Sines and Cosines

The video tutorial covers the application of the Law of Sines and the Law of Cosines to solve problems involving non-right triangles. It begins with an introduction to different types of triangles and explains the relationship between angles and their opposite sides. The tutorial provides detailed explanations and examples for both laws, demonstrating how to find missing sides and angles in triangles. The session concludes with a summary and encourages practice of the concepts discussed.

What theorem is applicable only to right triangles, as mentioned in the introduction?

• Euler's Formula

• Law of Sines

• Pythagorean Theorem

• Law of Cosines

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CCSS.8.G.B.8

Which law creates a proportion between the sine of angles and their opposite sides?

• Law of Tangents

• Pythagorean Theorem

• Law of Cosines

• Law of Sines

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In the Law of Sines, if angle A is 32 degrees and side a is 40, what is the sine of angle A over side a?

• sin(40)/32

• sin(32)/50

• sin(40)/32

• sin(32)/40

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which statement best describes the relationship between the sides and angles in the Law of Sines?

• The sine of an angle is inversely proportional to its opposite side.

• The tangent of an angle is directly proportional to its opposite side.

• The cosine of an angle is directly proportional to its opposite side.

• The sine of an angle is directly proportional to its opposite side.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is required to use the Law of Cosines effectively?

• Two sides and the included angle

• Three angles

• Two angles and one side

• At least one right angle

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

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

• Multiply the squares of the other two sides by the cosine of the opposite angle

• Divide the square of one side by the cosine of the opposite angle

• Subtract the squares of the other two sides from twice their product times the cosine of the opposite angle

• Add the squares of the other two sides and subtract twice their product times the cosine of the opposite angle

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the correct expression for the Law of Cosines?

• c^2 = a^2 + b^2 + 2ab cos(C)

• c^2 = a^2 + b^2 - 2ab cos(C)

• c = a + b - 2ab cos(C)

• c^2 = a^2 * b^2 - 2ab cos(C)

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

When solving for an angle using the Law of Cosines, what mathematical function is typically used?

• Cosine

• Cosine inverse

• Tangent

• Sine

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which scenario is most appropriate for using the Law of Sines?

• When all three angles are known

• When two angles and any side are known

• When two sides and the included angle are known

• When all three sides are known

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What does the Law of Cosines directly help to find?

• The radius of the circumscribed circle

• The height of a triangle

• The length of a side in a triangle

• The area of a triangle

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11