Understanding the Law of Cosines

This video tutorial covers the law of cosines, explaining its derivation and application in solving oblique triangles. It includes examples of solving triangles using given sides and angles, and demonstrates the use of both the law of cosines and the law of sines. The tutorial provides a detailed walkthrough of calculations and emphasizes recognizing patterns in the equations to aid memory.

What type of triangle is referred to as an oblique triangle?

• A triangle with two equal angles

• A triangle with all equal sides

• A triangle with no right angle

• A triangle with a right angle

Which of the following is a condition to apply the Law of Cosines?

• Two angles and a side are known

• All three angles are known

• Two sides and the included angle are known

• One side and one angle are known

In the Law of Cosines formula, what does the term 'b^2 + c^2 - 2bc cos(A)' represent?

• The length of side a squared

• The perimeter of the triangle

• The area of the triangle

• The sum of angles in the triangle

What is the key pattern to remember in the Law of Cosines formula?

• The product of all angles

• The sum of all angles

• The angle used in cosine is opposite the side on the left

• The sum of all sides

What is the first step in deriving the Law of Cosines?

• Calculating the area of the triangle

• Constructing an altitude in the triangle

• Using the Law of Sines

• Finding the perimeter of the triangle

In the derivation of the Law of Cosines, what theorem is applied to the right triangles formed?

• The Law of Tangents

• The Triangle Sum Theorem

• The Pythagorean Theorem

• The Law of Sines

In the first example problem, which form of the Law of Cosines is used to find side b?

• a^2 = b^2 + c^2 - 2bc cos(A)

• a^2 = b^2 + c^2 - 2bc cos(C)

• b^2 = a^2 + c^2 - 2ac cos(B)

• c^2 = a^2 + b^2 - 2ab cos(C)

After finding side b in the first example, which law is used to find angle A?

• The Pythagorean Theorem

• The Law of Sines

• The Law of Cosines

• The Law of Tangents

In the second example, which angle is calculated first using the Law of Cosines?

• Angle A

• Angle D

• Angle B

• Angle C

What is the final step in solving the triangle in the second example?

• Calculating the perimeter

• Using the Law of Sines to find another angle

• Applying the Pythagorean Theorem

• Finding the area of the triangle