The Law of Cosines

The video tutorial explains the law of cosines, comparing it to the Pythagorean theorem. It details how the law of cosines can be used to solve triangles when given two sides and the included angle (side-angle-side) or all three sides (side-side-side). The tutorial provides step-by-step examples for solving these types of triangles and highlights the differences between the law of sines and the law of cosines. The video concludes with a comprehension check to reinforce learning.

What is the main difference between the Pythagorean theorem and the law of cosines?

• The Pythagorean theorem applies to all triangles, while the law of cosines applies only to right triangles.

• The Pythagorean theorem is used for calculating angles, while the law of cosines is used for calculating areas.

• The Pythagorean theorem applies only to right triangles, while the law of cosines applies to any triangle.

• The Pythagorean theorem uses angles, while the law of cosines uses side lengths.

When using the law of cosines to solve a side-angle-side triangle, what information do you need?

• One side and one angle

• Two angles and one side

• Three sides

• Two sides and the angle between them

After finding the third side using the law of cosines, how can you find the remaining angles?

• Use the law of sines and subtract from 180 degrees

• Measure them directly

• Use the Pythagorean theorem

• Use the law of cosines again

What is the first step in solving a side-side-side triangle using the law of cosines?

• Find the shortest side

• Calculate the area of the triangle

• Use the law of sines

• Solve for the angle opposite the longest side

How do you find the third angle after using the law of cosines and the law of sines?

• Multiply the two known angles

• Divide the two known angles

• Add the two known angles

• Subtract the two known angles from 180 degrees