Pg. 435 Homework Pg. 443#1 – 10 all, 13 – 18 all #3ɣ = 110°, a = 12.86, c = 18.79#4No triangle possible #5α = 90°, ɣ = 60°, c = #6b = 4.61, c = 4.84, ɣ = 68° #7a = 3.88, c = 6.61, ɣ = 68° #8α = 41.62°, ɣ = 53.38°, c = 4.83 #10α = 29.51°, ɣ = °, c = #12α = 49.51°, ɣ = 14.49°, c = 3.62 #13No triangle possible#14No triangle possible #15α = 22.06°, ɣ = 5.94°, c = 2.20 #18a)54.60 ftb) ft apart # miles high

8.2 Law of Cosines Definition Law of Sines is best for when you have two angles and one side or when two sides and a non-included angle are given. Law of Cosines is best when you have two sides and the included angle (Law of Sines does not apply here!) Law of Cosines For any triangle ABC, labeled in the usual way Solve triangle ABC if a = 5, b = 3, ɣ = 35°. Solve triangle ABC if a = 9, b = 7, c = 5.

8.2 Law of Cosines Solving an Oblique Triangle Parts GivenNumber of Possible Triangles 1. Three Angles (sum equals 180°) Infinitely Many 2. Two Angles (sum less than 180°) and One Side One 3. One Angle, One Side Zero, One or Two 4. Three Sides (sum of any two greater than the third) One Area of Triangles Let ABC be a triangle labeled in the usual way. Then the area A of the triangle is given by:

8.2 Law of Cosines Heron’s Area Formula Let ABC be a triangle labeled in the usual way. Then the area A of the triangle is given by: where is one half the perimeter, or the semi-perimeter. Examples: Use the best method to find the area. Find the area of triangle ABC if a = 8, b = 5, ɣ = 52°. Find the area of triangle ABC if a = 9, b = 7, c = 5.