How to determine if you have 0,1 or 2 triangles for the ambiguous case

The video tutorial discusses the ambiguous case of side-side-angle in triangles, explaining how it can result in one, two, or no triangles. The teacher uses the law of sines to solve for a missing angle and demonstrates how to identify when no triangle exists due to an error domain. The tutorial also covers conditions under which one or two triangles can exist, emphasizing the importance of understanding these concepts in trigonometry and geometry.

What is the ambiguous case in triangle geometry?

• A situation where a triangle has three equal sides

• A scenario where a triangle has two right angles

• A triangle with all angles less than 60 degrees

• A case where a triangle can have one, two, or no solutions

Which law is used to solve for a missing angle in a triangle when given two sides and a non-included angle?

• Law of Sines

• Law of Cosines

• Law of Tangents

• Pythagorean Theorem

What does it mean if the sine inverse of a calculated value results in an error?

• The triangle is equilateral

• The triangle is isosceles

• The triangle is right-angled

• No triangle can be formed

Under what condition can two triangles exist in an ambiguous case?

• When the triangle has a right angle

• When all sides are equal

• When the calculated angle and its supplement both fit within the triangle

• When the sum of angles is exactly 180 degrees

What is the result if the sum of angles in a triangle is less than 180 degrees after calculating B prime?

• No triangle exists

• The triangle is equilateral

• One triangle exists

• Two triangles exist