Exploring the Law of Cosines in Triangles

The video tutorial explains how to solve triangles using the law of cosines and the law of sines. It begins with a side-angle-side triangle, demonstrating why the law of sines is not applicable and how to use the law of cosines to find the missing side. Once the side is found, the law of sines is used to determine the remaining angles. The tutorial then covers solving a side-side-side triangle, using the law of cosines to find the first angle and subsequently applying the law of sines to find the other angles. The video emphasizes understanding when to use each law based on the given triangle information.

Why can't the Law of Sines be used with one of each different letter?

• Because it requires two of the same letter

• Because it requires two angles and one side

• Because it requires two sides of the same letter

• Because it requires at least one complete set of side-angle pairs

What is the first step in using the Law of Cosines to solve for a side?

• Square all given sides

• Identify the given angles

• Use the formula involving the given angle and two sides

• Cross multiply to solve for the missing side

How do you find the length of side c using the Law of Cosines?

• c = sqrt(a^2 + b^2 - 2ab cos(C))

• c = a^2 + b^2 - 2ab cos(C)

• c = sqrt(a^2 + b^2)

• c = a + b - cos(C)

What is the correct formula for the Law of Cosines?

• c^2 = a^2 + b^2 - 2ab cos(C)

• a^2 = b^2 + c^2 - 2bc cos(A)

• Both A and B

• None of the above

After finding all sides, what method is used to find the missing angles?

• Law of Sines

• Trigonometric identities

• Pythagorean theorem

• Law of Cosines

How is angle B found using the Law of Sines after finding side c?

• sin(B) = B / sin(c)

• B = arcsin((c * sin(C)) / b)

• sin(B) = c / sin(C)

• B = arcsin(c / sin(C))

What indicates a triangle can be solved using the Law of Cosines?

• Two angles and one side are known

• All three sides are known

• Both B and C

• Two sides and the included angle are known

What is the result of angle C using the Law of Cosines with sides 7, 8, and 9?

• 60 degrees

• 73.4 degrees

• 90 degrees

• 45 degrees

Why is there only one possible solution for the triangle with sides 7, 8, and 9?

• Because it forms a right triangle

• Because angle A plus pre-existing angles exceeds 180 degrees

• Because the sum of angles in a triangle is always 180 degrees

• Because angle A cannot exceed 180 degrees

What is the final step in solving a triangle with all sides given?

• Verify the triangle inequality theorem

• Use the Law of Sines to find the remaining angles

• Calculate the area of the triangle

• Use the Law of Cosines again to find the remaining sides