Solving Triangles with the Law of Sines: The Ambiguous Case

This video tutorial on the Law of Sines focuses on the ambiguous case of side-side-angle (SSA) scenarios. It explains how the Law of Sines can yield 0, 1, or 2 solutions when given two sides and an angle. The video outlines the conditions necessary for two solutions and provides examples demonstrating no solution, one solution, and two solutions. Key points include understanding the sum of triangle angles, the sine function's range, and the importance of checking both acute and obtuse angles.

What is the sum of the interior angles of a triangle?

• 90 degrees

• 180 degrees

• 360 degrees

• 270 degrees

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CCSS.8.G.A.5

In which quadrants can the sine function return a positive value?

• First and Third Quadrants

• Third and Fourth Quadrants

• Second and Fourth Quadrants

• First and Second Quadrants

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CCSS.HSF.TF.A.2

For two solutions in SSA configuration, the given angle must be:

• Obtuse

• Right

• Straight

• Acute

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

If the sine of theta is greater than 1, how many solutions are there?

• 0

• 1

• 2

• Infinite

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CCSS.HSF.TF.B.7

What is the result of applying the Law of Sines if sine theta is less than 1?

• Cannot be determined

• Two possible solutions

• Exactly one solution

• No solution

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What indicates that there is no solution in a SSA configuration?

• Sine theta equals 0

• Sine theta is less than -1

• Sine theta is greater than 1

• Sine theta equals 1

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How do you determine the number of solutions when given side-side-angle?

• By using the Pythagorean theorem

• By finding both acute and obtuse angles

• By calculating the area of the triangle

• By comparing the given sides

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CCSS.7.G.A.2

What is the next step if an obtuse angle is possible in SSA configuration?

• The problem is unsolvable

• There are two solutions

• There is exactly one solution

• There are no solutions

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In SSA configuration, if the given angle is acute and sine theta is less than 1, what should you check for?

• If the triangle is a right triangle

• If the triangle is equilateral

• If an obtuse angle is possible

• If the sides are congruent

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What does it mean if the sum of the angles exceeds 180 degrees?

• The triangle is valid

• There is exactly one solution

• The triangle is invalid

• There are two solutions

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CCSS.7.G.A.2