Understanding the Law of Sines and the Ambiguous Case

This video tutorial covers the ambiguous case in the law of sines, focusing on solving triangles given side-side-angle. It explains the conditions under which there can be zero, one, or two solutions. The video includes animations and examples to illustrate these concepts, emphasizing the importance of understanding the sum of interior angles and the sine function's properties. Key points and example problems demonstrate scenarios with no solution, one solution, and two solutions, providing a comprehensive understanding of the topic.

What is the main challenge when using the Law of Sines with side-side-angle (SSA)?

• It requires all angles to be known.

• It only works for right triangles.

• It can result in 0, 1, or 2 solutions.

• It always results in no solution.

Which condition is NOT necessary for having two solutions in an SSA triangle?

• Side A must be greater than side B.

• Side A must be longer than the altitude.

• The given angle must be acute.

• The sum of angles must be 180 degrees.

If the sine of an angle calculated using the Law of Sines is greater than 1, what does this indicate?

• The triangle is equilateral.

• There are two solutions.

• There is one solution.

• There is no solution.

In the example where angle A is 88 degrees, what is the calculated angle C?

• 151 degrees

• 88 degrees

• 63 degrees

• 29 degrees

What is the length of side B in the example where angle A is 88 degrees and side A is 110 feet?

• 98 feet

• 63 feet

• 54 feet

• 110 feet

In the scenario with angle B as 40 degrees and side B as 22 cm, what is the possible obtuse angle A?

• 40 degrees

• 119 degrees

• 61 degrees

• 21 degrees

When solving for two possible triangles, what must be true about the sum of the angles?

• It must be exactly 180 degrees.

• It must be less than 180 degrees.

• It must be more than 180 degrees.

• It must be exactly 90 degrees.

What is the length of side C in the first solution where angle A is 61 degrees?

• 22 cm

• 34 cm

• 37 cm

• 12 cm

In the second solution where angle A is 119 degrees, what is the length of side C?

• 34 cm

• 22 cm

• 12 cm

• 37 cm

What is the key to finding the second solution in an SSA problem?

• Using only obtuse angles.

• Using only acute angles.

• Ensuring all sides are equal.

• Finding both acute and obtuse angles with the same sine value.