Exploring the Ambiguous Case of the Law of Sines

The video tutorial covers the ambiguous case of the Law of Sines, explaining when and how it applies. It demonstrates solving two possible triangles when the side opposite the given angle is less than the adjacent side. The tutorial includes detailed steps for calculating angles and side lengths using the Law of Sines, with examples illustrating when two triangles exist and when only one does. The video emphasizes understanding supplementary angles and using inverse sine functions to find unknown angles.

What condition leads to the ambiguous case in the Law of Sines?

• The given angle is acute.

• The given angle is obtuse.

• The side opposite the given angle is shorter than the adjacent side.

• The side opposite the given angle is longer than the adjacent side.

How do you find the measure of an unknown angle using the Law of Sines?

• Multiply both sides by the sine of the given angle.

• Divide the sine of the given angle by the opposite side.

• Take the sine inverse of the product of sine of the given angle and its opposite side.

• Add the sine of the given angle to the opposite side.

What is the measure of angle B in the first possible triangle?

• 81.8 degrees

• 65.2 degrees

• 114.8 degrees

• 32.2 degrees

How is the measure of angle B in the second triangle found?

• By adding 65.2 to 180

• By subtracting 65.2 from 180

• By dividing 180 by 65.2

• By multiplying 65.2 by 2

What is the length of side C in the first triangle?

• 2.5

• 5.9

• 10.9

• 9.6

What is the measure of angle B in the second example's first triangle?

• 105.6 degrees

• 135.6 degrees

• 44.4 degrees

• 14.4 degrees

In the second example, how many triangles exist based on the given sides and angle?

• None

• One

• Two

• Three

What is the length of side B in the second triangle of the second example?

• 5.9

• 2.5

• 10.9

• 9.6

In the scenario where only one triangle is possible, what is the measure of angle C?

• 113.3 degrees

• 26.7 degrees

• 40 degrees

• 14.3 degrees

What is the length of side C in the scenario with only one possible triangle?

• 2.5

• 9.6

• 5.9

• 14.3