Law of Cosines and Triangle Solutions

This video tutorial introduces the Law of Cosines, explaining its derivation and application in solving oblique triangles. It covers the conditions for using the Law of Cosines, such as side-angle-side and side-side-side scenarios. The video provides a proof of the theorem using right triangles and demonstrates solving triangles with practical examples. It also discusses using the Law of Sines in conjunction with the Law of Cosines to find missing angles. The tutorial concludes with advanced problem-solving strategies and directs viewers to additional resources for further learning.

What type of triangle is specifically addressed by the Law of Cosines?

• Oblique triangle

• Isosceles triangle

• Right triangle

• Equilateral triangle

Which of the following is a requirement for using the Law of Cosines?

• Two angles and a side

• Three angles

• Two sides and an included angle

• One side and one angle

In the Law of Cosines, what is the relationship between the angle and the side opposite to it?

• The side opposite the angle is on the same side of the equal sign

• The angle is always smaller than the side

• The side opposite the angle is on the other side of the equal sign

• The angle is always larger than the side

What geometric method is used to derive the Law of Cosines?

• Constructing a bisector

• Constructing an altitude

• Constructing a median

• Constructing a tangent

Which theorem is applied in the derivation of the Law of Cosines?

• Theorem of Congruence

• Theorem of Similarity

• Pythagorean Theorem

• Theorem of Proportions

In the first example problem, what is the approximate length of side B?

• 43.7 feet

• 43.4 feet

• 32.2 feet

• 24.2 feet

After using the Law of Cosines, which law is used to find the missing angles?

• Law of Cotangents

• Law of Sines

• Law of Secants

• Law of Tangents

In the second example, which angle is recommended to find first?

• The largest angle

• The angle opposite the largest side

• The angle opposite the smallest side

• The smallest angle

What is the approximate measure of angle C in the second example?

• 73.1 degrees

• 112.5 degrees

• 25.7 degrees

• 41.8 degrees

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

• Calculating the perimeter of the triangle

• Using the Law of Cosines again

• Using the Law of Sines to find the last angle

• Finding the area of the triangle