The Law of Cosines (8.2.1)

Question 1

• Like the law of sines, the law of cosines is a formula that solves for angles and sides for any given triangle, even those that are not right triangles. It is derived from the Pythagorean theorem.

Answer 1

• Like the law of sines, the law of cosines is a formula that solves for angles and sides for any given triangle, even those that are not right triangles. It is derived from the Pythagorean theorem.

Question 2

• The law of cosines is used to solve a triangle when given three sides of a triangle or two sides plus the included angle.

Answer 2

• The law of cosines is used to solve a triangle when given three sides of a triangle or two sides plus the included angle.

Question 3

• The law of cosines has three forms. In every case, the last term is 2 times the product of the two sides with the cosine of the included angle. The single term on the left is always the square of the side opposite the angle. Use the form of the identity that fits what is known about the triangle. In a triangle with sides a, b, c, and opposite angles α, β, γ:

a^2 = b^2 + c^2 - 2bcosα 
b^2 = a^2 + c^2 - 2acosβ 
c^2 = a^2 + b^2 - 2abcosγ

Answer 3

• The law of cosines has three forms. In every case, the last term is 2 times the product of the two sides with the cosine of the included angle. The single term on the left is always the square of the side opposite the angle. Use the form of the identity that fits what is known about the triangle. In a triangle with sides a, b, c, and opposite angles α, β, γ:

a^2 = b^2 + c^2 - 2bcosα 
b^2 = a^2 + c^2 - 2acosβ 
c^2 = a^2 + b^2 - 2abcosγ