Law of Cosines and Sines Concepts

The video tutorial covers the Law of Cosines, starting with a recap of the Law of Sines. It explains the formulas for the Law of Cosines and demonstrates how to solve triangles using these formulas. Two examples are provided: one where two sides and an angle are given, and another where all sides are given. The tutorial emphasizes the importance of finding the largest angle with the Law of Cosines and the smallest angle with the Law of Sines.

What is required to use the Law of Sines to solve a triangle?

• Two angles and one side

• Three sides

• One angle and its corresponding side

• Two sides and one angle

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

• 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)

• a^2 = b^2 - c^2 - 2bc * cos(A)

In the Law of Cosines, which sides and angles are matched up?

• The two given sides and the included angle

• The side being solved for and the adjacent angle

• The two given angles and the included side

• The side being solved for and the angle opposite it

What is the first step in solving a triangle using the Law of Cosines?

• Find the largest side

• Find the smallest side

• Find the largest angle

• Find the smallest angle

When solving for side 'a' using the Law of Cosines, which formula is used?

• 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 * cos(A)

• a^2 = b^2 - c^2 - 2bc * cos(A)

What is the approximate value of side 'a' in the first example?

• 6.44

• 10

• 38

• 6

What is the next step after finding the largest angle using the Law of Cosines?

• Find the largest side using the Law of Sines

• Find the smallest side using the Law of Sines

• Find the smallest angle using the Law of Sines

• Find the smallest angle using the Law of Cosines

In the second example, what is the largest angle found using the Law of Cosines?

• 125.1 degrees

• 106.95 degrees

• 38 degrees

• 24.15 degrees

What is the final step in solving a triangle once two angles are known?

• Add the known angles to find the third angle

• Use the Law of Cosines to find the third angle

• Subtract the known angles from 180 degrees

• Use the Law of Sines to find the third angle

Which rule is followed when finding angles using the Law of Sines?

• Find the smallest angle first

• Find the largest angle first

• Find the smallest side first

• Find the largest side first