Exploring the Law of Sines

What is the Law of Sines used for in trigonometry?

• To find side lengths and angles in any triangle

• To measure the circumference of circles

• To calculate angles in right triangles

• To define the ratios of sides in a square

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What does the Law of Sines relate in a triangle?

• The sine of an angle and the length of its opposite side

• The sine of an angle and the length of the adjacent side

• The tangent of an angle and the length of the adjacent side

• The cosine of an angle and the length of its opposite side

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which of the following is NOT a component of the Law of Sines ratio?

• Length of the adjacent side

• Length of the opposite side

• All are components

• Sine of an angle

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

When using the Law of Sines, how many ratios are typically used at a time?

• Three

• One

• Two

• Four

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In the provided example, what is the first step to find the missing side YZ?

• Calculate the sine of angle Z

• Divide the sine of 77 by 7

• Identify a known angle and its opposite side

• Multiply the sines of all known angles

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What mathematical method is used to solve for YZ in the example?

• Addition

• Subtraction

• Cross multiplication

• Division

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CCSS.HSG.SRT.B.4

Why is it important to use original given values in calculations?

• To make the problem more complex

• To use the calculator less

• To make calculations simpler

• To avoid rounding errors

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CCSS.5.MD.A.1

What is the correct way to solve for an angle using the Law of Sines?

• Use sine inverse on the ratio of sides

• Multiply the sines of known angles

• Add the lengths of the sides

• Divide the longest side by the sine of its opposite angle

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Why can't the Pythagorean theorem be used in the scenarios discussed?

• It is too complex for such problems

• It cannot calculate angles

• It is only for circles

• It only applies to right triangles

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CCSS.8.G.B.8

What is the result of solving the triangle in the example using the Law of Sines?

• Neither sides nor angles are found

• Both sides and angles are found

• Only the angles are found

• Only the sides are found

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11