Presentation Transcript

1. 14.4 The Law of Sines14.5 Law of Cosines

   Objectives: To find the area of any triangle and use the Law of Sines To use the Law of Cosines in finding the measures of sides and angles of a triangle.
2. Law of Sines Use the Law of Sines to find the missing sides of oblique (NOT RIGHT) triangles. AAS, ASA, & SSA(The ambiguous case) B a c A C b
3. Solving Oblique Triangles Example 1: Solve triangle ABC if A = 33°, B = 105°, and b=37.9.
4. Solving Oblique Triangles Example 2: Solve triangle ABC if A = 22.5°, B = 96°, and c=30.
5. Example 3: Solve the triangle if A=42°, a = 22, b = 12.
6. Area of Triangles You need to have SAS to use this formula. B A C
7. Finding the Area of a Triangle Example 3) Find the area of triangle ABC if a=4.7, c=12.4, and B=47°.
8. You Try: Find the area of triangle DEF if d=13.9, D=34.4°, and E=14.8°.
9. Homework 14.4 P 804: 5, 9, 11, 17, 19, 31, 33
10. Law of Cosines The Law of Cosines is used to find missing sides and angles of oblique triangles. SSS & SAS B c a b A C
11. Find all missing sides and angles for each triangle. Example 4) For ∆ABC, A = 120°, b = 9, c = 5
12. Find all missing sides and angles for each triangle. Example 5) For ∆ABC, a = 24, b = 40, c = 18
13. Homework 14.5 P 810 – 811: 3, 5, 7, 9, 24, 25