Exploring the Sine Law in Acute Triangles

This video tutorial explains the relationship between angles and their opposite sides in triangles, focusing on the sine law for acute triangles. It demonstrates how the sine law can be used to solve problems by finding unknown angles or side lengths. The tutorial includes examples and discusses the limitations of the sine law, particularly when it cannot be applied. The video concludes with a summary of the key points covered.

What is the maximum degree any angle in an acute triangle can have?

• 180 degrees

• More than 90 degrees

• Exactly 90 degrees

• Less than 90 degrees

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CCSS.8.G.A.5

According to the sine law, how are the angles and their opposite sides related?

• Not related

• Equal to each other

• Inversely proportional

• Directly proportional

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In the given example, what is the value of K when the side opposite to 68 degrees is 6 units?

• 68 units

• 54 units

• 6 units

• Approximately 5.24 units

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which scenario is not suitable for applying the sine law?

• Two side lengths and the included angle known

• All side lengths known

• Two angles and one side length known

• One angle and two side lengths known

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the value of angle X when using the sine law in the example?

• 40.7 degrees

• 78 degrees

• 54 degrees

• 60 degrees

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How do you find the value of angle Z in the triangle?

• 180 minus the sum of the other two angles

• Multiply the other two angles

• None of the above

• Sum of the other two angles

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CCSS.8.G.A.5

What is the approximate value of angle Z?

• 40.7 degrees

• 180 degrees

• 61.3 degrees

• 78 degrees

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CCSS.8.G.A.5

Which formula could you use to find the length of side C?

• Neither A nor B

• Both A and B

• Sine of 40.7 over 4 equals sine of 61.3 over C

• Sine of 78 over 6 equals sine of 61.3 over C

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What impact does rounding off the angles have on the accuracy of your calculations?

• Changes the triangle type

• Makes them less accurate

• Makes them more accurate

• No impact

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CCSS.HSF.TF.A.1

If angles were not rounded off, how would the answers using different formulas compare?

• Cannot be determined

• They would be identical

• They would be different

• They would be inversely proportional

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11