Understanding the Ambiguous Case in the Law of Sines

The video tutorial covers the ambiguous case in the law of sines, focusing on how to determine the number of possible triangles given certain conditions. It begins with a review of calculating the altitude of a triangle using trigonometry, then explains the ambiguous case, also known as the SSA condition. The tutorial outlines different scenarios, including when no triangle, one triangle, or two triangles can be formed, and provides step-by-step solutions for each case. The video concludes with examples and exercises to reinforce the concepts.

What is the first step in finding the altitude of a triangle using trigonometry?

• Use the secant function

• Use the tangent function

• Use the sine function

• Use the cosine function

In the context of the ambiguous case, what does the 'donkey rule' refer to?

• An angle followed by two sides

• An angle followed by three sides

• Three sides

• Two angles and a side

Which scenario results in no triangle being formed in the ambiguous case?

• When side a is equal to side b

• When side a is greater than side b

• When side a is equal to the height

• When side a is less than the height

How many triangles can be formed if side a is greater than side b in an acute angle scenario?

• None

• One

• Three

• Two

What is the result when side a is equal to the height in the ambiguous case?

• An isosceles triangle

• No triangle

• One right triangle

• Two triangles

In the example where angle A is 42 degrees, what is the length of side C?

• 22

• 12

• 29.4

• 8.02

What is the angle B in the example where angle A is 20.5 degrees and side B is 31?

• 94.7 degrees

• 38.5 degrees

• 21.4 degrees

• 64.8 degrees

In the second example of two triangles, what is the length of side C?

• 23.9

• 10.2

• 34.2

• 27.4

What condition must be met for two triangles to be possible in the ambiguous case?

• Side a is greater than the height but less than side b

• Side a is greater than side b

• Side a is less than the height

• Side a is equal to side b

In the homework example, what is the height when angle B is 25 degrees and side a is 5?

• 3.5

• 5

• 4.2

• 2.11