Notes Over 8.2 Solving Oblique Triangles To solve an oblique triangle, you need to be given one side, and at least two other parts (sides or angles). 4 cases for oblique triangles A B C a b c 1. Two angles and any side (AAS or ASA) 2. Two sides and an angle opposite one of them (SSA) 3. Three sides (SSS) 4. Two sides and their included angle (SAS) The first two cases use Law of Sines, the last two will use the Law of Cosines.

Notes Over 8.2 Law of Cosines If ABC is a triangle with sides a, b, c, then according to the law of cosines,

The SAS Case Solve ∆ABC Find:

The SAS Case Solve ∆ABC Find: Notes Over 8.2

Law of Cosines If ABC is a triangle with sides a, b, c, then according to the law of cosines, Notes Over 8.2

The SSS Case Solve ∆ABC Find:

The SSS Case Solve ∆ABC Find: Notes Over 8.2

5. The pitcher’s mound on a softball field is 43 feet from home plate and the distance between the bases is 60 feet. (The pitcher’s mound is not halfway between home plate and second base.) How far is the pitcher’s mound from first base? P H F h 45 o

Notes Over 8.2 Heron’s Area Formula For any triangle, given three sides 6.Find the area of a triangular region having sides of length 43 meters, 53 meters, and 72 meters.

Notes Over 8.2 Pg. 595, 8.2 #1-16, all