Law of Cosines

Used when Law of Sines doesn’t work

Formula: leg^2 = adj leg^2 + other adj leg^2 – 2( adj leg)(other adj) cos(angle between)

Ex 1. On triangle ABC side a =7, side c = 3, and angle B = 130 degrees. Find side b, angle A, and angle C

To find side b: b^2 = 3^2 + 7^2 -2(3)(7) cos130 degrees

Square root both sides and b = 9.219cm

7^2 = 3^2 + 9.219^2 – 2(3)(9.219)cosA

-2(3)(9.219)cosA = 7^2-3^2-9.219^2

cosA = ((7^2-3^2-9.219^2)/(-2(3)9.219))

A = cos^-1((7^2-3^2-9.219^2)/(-2(3)9.219))

Angle A = 35.574 degrees

130 + 35.574 = 165.574 – 180 = 14.426

Angle C = 14.426 degrees