Ambiguous Cases in Triangle Problems

This video tutorial explains the ambiguous case in triangle geometry, where given information can lead to two possible triangles. It uses the sine law to identify and solve these cases, providing examples to illustrate the concept. The video encourages viewers to practice more problems to solidify their understanding.

What is the ambiguous case in triangles?

• A situation where two different triangles can be formed.

• A situation where exactly one triangle can be formed.

• A situation where no triangle can be formed.

• A situation where more than two triangles can be formed.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What should you compare to determine if the ambiguous case occurs?

• The area of the triangle.

• The lengths of the sides next to and opposite the given angle.

• The angles of the triangle.

• The perimeter of the triangle.

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CCSS.7.G.A.2

If the side opposite the given angle is longer than the side next to the angle, how many triangles can be formed?

• Three

• One

• Two

• None

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the sine law formula used in solving ambiguous cases?

• cos A / a = cos B / b

• sin A / a = sin B / b

• cot A / a = cot B / b

• tan A / a = tan B / b

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CCSS.HSG.SRT.C.8

In the first example, what is the height of the triangle when the angle is 36 degrees and the hypotenuse is 8?

• 4.7

• 5.2

• 6.1

• 7.3

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the first angle B found in the first example using the sine law?

• 80.1 degrees

• 70.1 degrees

• 60.1 degrees

• 90.1 degrees

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CCSS.HSG.SRT.C.8

In the second example, what is the height of the triangle when the angle is given and the hypotenuse is 7?

• 8.43

• 7.43

• 6.43

• 5.43

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the second angle B found in the second example using the sine law?

• 133.33 degrees

• 123.33 degrees

• 143.33 degrees

• 113.33 degrees

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the key step to confirm the second case in an ambiguous situation?

• Checking if the sum of the two angles is exactly 180 degrees.

• Checking if the sum of the two angles is more than 180 degrees.

• Checking if the sum of the two angles is less than 180 degrees.

• Checking if the sum of the two angles is less than 90 degrees.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What should you do after identifying an ambiguous case?

• Check for more than two triangles.

• Assume only one triangle exists.

• Solve for the two different angles that produce the two triangles.

• Ignore the case.

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11