Law of Cosine Video Notes

What is the correct formula to use when you have a side-angle-side triangle and need to find the missing side?

• a^2 = b^2 + c^2 - 2bc cos(A)

• c^2 = a^2 + b^2 - 2ab cos(C)

• b^2 = a^2 + c^2 - 2ac cos(B)

• a^2 + b^2 = c^2

What is the value of side c when side a is 10, side b is 20, and angle C is 60 degrees?

• 10√3

• 17.32

• 20√2

• 15

Why can't the Law of Sines be used initially to solve the triangle with sides a=10, b=20, and angle C=60 degrees?

• Because it only works for right triangles

• Because we have all three sides

• Because it requires two angles and one side

• Because we don't have any angles except angle C

What is the value of angle B after finding side c to be 17.32 in the triangle with sides a=10, b=20, and angle C=60 degrees?

• 30 degrees

• 60 degrees

• 45 degrees

• 90 degrees

How do you find the value of angle A after determining angle B is 90 degrees and angle C is 60 degrees?

• Multiply angles B and C

• Use the Law of Sines with side a

• Subtract the sum of angles B and C from 180

• Add angles B and C and subtract from 360

What formula is used to find the cosine of angle C when you have all three sides of a triangle?

• cos(C) = (a^2 + b^2 - c^2) / 2ab

• cos(C) = (c^2 - a^2 - b^2) / -2ab

• cos(C) = (a^2 + b^2 + c^2) / 2ab

• cos(C) = (c^2 + a^2 + b^2) / 2ab

What is the value of angle C when sides a=7, b=8, and c=9?

• 45 degrees

• 90 degrees

• 60 degrees

• 73.4 degrees

After finding angle C to be approximately 73.4 degrees using the Law of Cosines, what method is suggested to find the other angles?

• Use the Pythagorean theorem

• Use trigonometric identities

• Use the Law of Sines

• Use the Law of Cosines again

What is the value of angle A when side a=7, side c=9, and angle C is approximately 73.4 degrees?

• 30 degrees

• 60 degrees

• 48.2 degrees

• 90 degrees

How do you determine the impossibility of a second triangle when finding angle A to be 48.2 degrees?

• By calculating the area of the triangle

• By verifying if angle A is acute

• By using the Law of Cosines

• By checking if the sum of angles exceeds 180 degrees