Law of Sines and Triangle Properties

This video tutorial demonstrates how to solve a triangle using the Law of Sines. It begins by labeling the angles and sides, then sets up a proportion to find unknown values. The tutorial walks through calculating angle B using inverse sine and determining angle A by subtracting known angles from 180 degrees. Finally, it calculates the length of side A using the Law of Sines, ensuring all angles and sides are solved. The video concludes with a summary of the process.

What is the first step recommended when solving a triangle using the Law of Sines?

• Find the perimeter of the triangle

• Label all angles and sides

• Calculate the area of the triangle

• Convert all angles to radians

Which angle's measure is initially known in the given triangle problem?

• Angle C

• Angle A

• Angle B

• None of the angles

What is the unknown variable in the initial proportion set up using the Law of Sines?

• Length of side A

• Measure of angle B

• Length of side C

• Measure of angle A

After calculating sine B, what mathematical function is used to find the measure of angle B?

• Cosine

• Inverse Cosine

• Tangent

• Inverse Sine

What is the approximate measure of angle B after calculation?

• 62.2 degrees

• 15.8 degrees

• 102 degrees

• 45 degrees

How do you determine the measure of angle A once angle B is known?

• Add angles B and C

• Multiply angles B and C

• Subtract angles B and C from 180 degrees

• Divide angle C by angle B

What is the sum of the interior angles of a triangle?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

Which ratio is used again to determine the length of side A?

• Sine A divided by A

• Sine B divided by B

• Sine C divided by C

• Cosine C divided by C

What is the approximate length of side A after calculation?

• 16.3 meters

• 10 meters

• 5 meters

• 18 meters

What is the final step in solving the triangle using the Law of Sines?

• Finding the area of the triangle

• Verifying the sum of angles

• Ensuring all angles and sides are determined

• Converting angles to radians