Law of Sines and

Cosines

Accelerated Math 3

You should know…

•Solving a triangle means finding all sides and angles.•Law of Sines and Cosines work for all triangles – not just right triangles.

Law of Sines

a

b

c

A

B

C

a b c

SinA SinB SinC

Ex. 1: Solve the triangle with C = 102.3o, B = 28.7o and b = 27.4 ft. (Given AAS)

Law of cosines

•a2 = b2 + c2 – 2bcCosA•b2 = a2 + c2 – 2acCosB•c2 = a2 + b2 – 2abCosC

b

ac

A

B

C

Ex. 2: Find all the angles. (Given SSS)• a = 8 ft, b = 19 ft and c = 14 ft

Ex. 3: Find the missing measures. (Given SAS)• A = 115o, b = 15 cm and c = 10 cm