Law of Cosines and Triangle Properties

The video tutorial explains the law of cosines, a method used for solving non-right triangles. It covers when to use the law of cosines, particularly in cases where you have three sides or two sides and the included angle. The tutorial provides formulas and highlights patterns in triangles to help remember them. Two examples are demonstrated: one using side-angle-side and another using side-side-side, showing step-by-step calculations to find unknown sides or angles. The video concludes by suggesting the use of the law of sines for further angle calculations.

When should you use the Law of Cosines?

• When you have only one side

• When you have two angles

• When you have a non-right triangle

• When you have a right triangle

What are the two scenarios where the Law of Cosines is applicable?

• Angle-Angle-Side and Side-Side-Side

• Side-Side-Side and Angle-Angle-Side

• Side-Angle-Side and Angle-Angle-Side

• Side-Side-Side and Side-Angle-Side

In a triangle, which letters represent the sides?

• Lowercase letters

• Uppercase letters

• Roman numerals

• Greek letters

What is the relationship between angle A and side a in a triangle?

• They are adjacent to each other

• They are opposite each other

• They are the same length

• They form a right angle

In the side-angle-side example, what is the value of angle C?

• 90 degrees

• 45 degrees

• 30 degrees

• 60 degrees

What is the length of side C in the side-angle-side example?

• 4

• 8

• 4√3

• 16

In the side-side-side example, what are the given side lengths?

• 3, 4, 5

• 5, 6, 7

• 7, 8, 9

• 6, 7, 8

What is the value of angle C in the side-side-side example?

• 70 degrees

• 90 degrees

• 60 degrees

• 78.5 degrees

After finding one angle using the Law of Cosines, which law can be used to find the other angles?

• Law of Secants

• Law of Sines

• Law of Tangents

• Law of Cotangents

What is the next step after finding the cosine of an angle in the Law of Cosines?

• Multiply by 2

• Divide by 2

• Take the sine inverse

• Take the cosine inverse