Law of Cosines and Sines Concepts

Professor Dave explains the law of cosines, comparing it to the Pythagorean theorem. He describes how it applies to any triangle, allowing calculation of a missing side when two sides and the included angle are known. The video covers solving side angle side and side side side triangles using the law of cosines, and how to find angles using known side lengths. The law of sines is also mentioned for solving additional angles. The video concludes with a comprehension check.

What is the main difference between the Pythagorean theorem and the Law of Cosines?

• Both theorems apply only to right triangles.

• The Pythagorean theorem applies only to right triangles, while the Law of Cosines applies to all triangles.

• Both theorems apply to all triangles.

• The Pythagorean theorem applies to all triangles, while the Law of Cosines applies only to right triangles.

Which of the following is the correct formula for the Law of Cosines?

• A^2 = B^2 + C^2 + 2BC sin A

• A^2 = B^2 + C^2 + 2BC cos A

• A^2 = B^2 + C^2 - 2BC sin A

• A^2 = B^2 + C^2 - 2BC cos A

In which type of triangle can the Law of Cosines be used to find the third side when two sides and the included angle are known?

• Isosceles triangle

• Side-angle-side triangle

• Equilateral triangle

• Right triangle

What additional information is needed to use the Law of Sines after applying the Law of Cosines to find a side?

• One angle and its corresponding side

• The length of the longest side

• The perimeter of the triangle

• The measure of the smallest angle

When solving a side-side-side triangle, which angle is it easiest to solve for first using the Law of Cosines?

• The angle opposite the middle side

• Any angle

• The angle opposite the longest side

• The angle opposite the shortest side

What is the next step after finding one angle using the Law of Cosines in a side-side-side triangle?

• Use the Pythagorean theorem to find another side

• Calculate the area of the triangle

• Use the Law of Sines to find another angle

• Find the perimeter of the triangle

How can the Law of Sines be used after applying the Law of Cosines to find an angle?

• To find the length of the longest side

• To find the perimeter of the triangle

• To find the area of the triangle

• To find another angle

What is the final step in solving a triangle using both the Law of Sines and the Law of Cosines?

• Using the Pythagorean theorem to verify the sides

• Calculating the perimeter of the triangle

• Finding the area of the triangle

• Subtracting the known angles from 180 degrees to find the third angle

Which law is more suitable for solving a triangle when all three sides are known?

• None of the above

• Law of Sines

• Pythagorean theorem

• Law of Cosines

What is the primary advantage of using the Law of Cosines over the Law of Sines?

• It can solve for angles in right triangles only.

• It can be used when no angles are known.

• It is simpler to use in all cases.

• It can solve for sides in equilateral triangles only.