Decoding the Ambiguous Case of the Law of Sines

What does the ambiguous case of the law of sines involve?

• Two angles and one side of a triangle

• An angle and two sides of a triangle

• Two sides and the angle between them

• Three angles of a triangle

What is the first step when given an acute angle in the ambiguous case?

• Compare the given sides

• Solve using the law of cosines

• Draw a specific picture as described

• Calculate the height of the triangle

What happens if the side opposite the angle is greater than the other given side?

• It's impossible to determine without further calculation

• No triangle is possible

• Exactly one triangle is possible

• Two triangles are possible

What does the height calculation involve in the ambiguous case?

• Multiplying the given side by the cosine of the angle

• Dividing the given side by the cosine of the angle

• Dividing the given side by the sine of the angle

• Multiplying the given side by the sine of the angle

How many outcomes are possible when given an obtuse angle in the ambiguous case?

• One

• Two

• It depends on the side lengths

• Three

In the example problem, what was the first thing checked after drawing the triangle?

• If the opposite side is greater than the height

• If the opposite side is less than the other side

• The height of the triangle

• The sine of the given angle

What indicates a two-triangle scenario in the ambiguous case?

• The opposite side is less than the height

• The height is greater than the opposite side

• The height is less than the opposite but greater than the other side

• The opposite side is greater than the height but less than the other side

How do you find the second possible angle in a two-triangle scenario?

• By subtracting the first angle from 180

• By adding the first angle to 180

• By finding the supplement of the first angle

• By recalculating using the law of sines

What is the relationship between B sub 1 and B sub 2 in the example?

• B sub 2 is the supplement of B sub 1

• B sub 2 is the inverse sine of B sub 1

• B sub 1 and B sub 2 are equal

• B sub 2 is twice B sub 1

What method is used to solve for side lengths in the example problem?

• Trigonometric ratios

• Law of sines

• Law of cosines

• Pythagorean theorem