Section 10.1: Non-right Triangles: Law of Sines

What is the Law of Sines used for in trigonometry?

• To solve oblique triangles

• To calculate the hypotenuse of a right triangle

• To find the radius of a circle

• To define the relationship between the sides and angles of a parallelogram

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which scenario is an example of using the Law of Sines?

• Measuring the height of a building using a right triangle

• Determining the volume of a sphere

• Calculating the circumference of a circle

• Finding the area of an oblique triangle using the sine function

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What must be known to solve an oblique triangle using the Law of Sines?

• The area of the triangle

• Two sides and all three angles

• Only the three angles of the triangle

• At least one side and any two angles

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What does the Law of Sines equation fundamentally relate?

• The sum of the angles in any triangle

• The ratio of an angle's sine to its opposite side

• The ratio of a side to its adjacent angle

• The difference between the angles and sides

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In which type of triangle is the Law of Sines particularly useful?

• Isosceles triangles

• Right triangles

• Equilateral triangles

• Oblique triangles

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is an ambiguous case in the context of the Law of Sines?

• A scenario where only right triangles are involved

• A case where no triangle exists

• A situation where two different triangles could satisfy the given conditions

• A condition where all angles are known but no sides

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How is the area of an oblique triangle calculated using the Law of Sines?

• Through the sum of all sides divided by the diameter

• By multiplying the base and height

• Applying Pythagoras' theorem

• Using the product of two sides and the sine of their included angle

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

CCSS.HSG.SRT.D.9

What is required to solve for two unknown sides in an AAS triangle scenario?

• One angle and one side

• Three sides and no angles

• Two angles and any side

• Two sides and one angle

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which of the following is NOT a possible outcome for SSA triangles?

• Two solutions

• Three solutions

• No solution

• One solution

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the first step in solving an oblique triangle using the Law of Sines?

• Calculating the area of the triangle

• Finding the diameter of the circumscribed circle

• Identifying at least three known values including one side

• Determining the height of the triangle

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11