Exploring the Ambiguous Case of the Law of Sines

What is the ambiguous case in triangle solving?

• Angle-Side-Angle

• Side-Side-Angle

• Angle-Angle-Side

• Side-Angle-Side

What happens if the side opposite the obtuse angle is the longest?

• No triangle is possible

• Exactly one triangle is possible

• Two triangles are possible

• Error in calculation

What does it indicate if a side is shorter than the altitude in a triangle setup?

• One triangle is possible

• Two triangles are possible

• No triangle is possible

• Infinite triangles are possible

How do you determine the number of triangles possible when given two sides and an acute angle?

• Using the Law of Cosines

• Calculating the altitude

• By comparing side lengths

• Rotating the side like a hinge

What is the result when the side across from the acute angle is longer than the adjacent side?

• Two triangles are possible

• No triangle is possible

• One triangle is possible

• The calculation is undetermined

What does an error message in the calculator typically indicate in triangle calculations?

• An obtuse angle is present

• The sides are congruent

• A right triangle has formed

• No triangle can be formed

In the Law of Sines, what does the sine of an angle over a side represent?

• The relationship between angle and opposite side

• The proportion of adjacent sides

• The ratio of opposite angles

• The calculation of the hypotenuse

What type of triangle is formed when two sides are congruent?

• Equilateral

• Isosceles

• Acute

• Scalene

How do you find the third angle in a triangle if two angles are known?

• Use the Law of Sines

• Add the two known angles and subtract from 180

• Multiply the two known angles

• Divide 180 by the sum of the two known angles

What method is used to solve for sides in different triangle configurations?

• Pythagorean Theorem

• Law of Tangents

• Law of Cosines

• Law of Sines