13.4 L AW OF S INES 13.5 L AW OF COSINES Algebra II w/ trig

I. Area of a Triangle When we know the measures of two sides ad the included angle:

A. Find the area of triangle ABC to the nearest tenth A C B 54 A B C 32

II. Law of Sines If you now at least one side and two other values. 1. two angles and any side (AAS, ASA) 2. two sides and an angle opposite one of them (SSA) --Ambiguous Case (0-1-2 Triangles) LAW OF SINES:

III. Law of Cosines 1. know the measures of two sides and the included angle 2. know the measures of three sides LAW OF COSINES: a 2 = b 2 + c 2 – 2bc cos A b 2 = a 2 + c 2 – 2ac cos B c 2 = a 2 + b 2 – 2ab cos C

IV. Decide whether to use Law of Sines or Law of Cosines? Then solve the triangle. 1. A = 46.3 degrees, a = 35, b = A = 78.3 degrees, b = 7, c = A = 29 degrees, b = 13, a = 6 4. C = 35 degrees, a = 18, b = B = 46.6 degrees, C =112 degrees, b = 13