1. Section 6.1 – Law of Sines Objective: TSWBAT use the Law of Sines and areas of oblique triangles to solve real-life problems. PA Common Core Standards: CC.2.2.HS.D.1 - Interpret the structure of expressions to represent a quantity in terms of its context.

2. Def: Oblique Triangle: a non-right triangle. LAW OF SINES:

3. AAS Example: Solve the triangle if C =102.3°, B = 28.7° and b = 27.4 ft. SSA leads to the Ambiguous Case. When we solve for an ANGLE, the ambiguous case appears. There can be one, two or no such triangles that exist.

4. Case 1) Single Solution Case: Solve the triangle with a = 22”, b = 12” and A = 42°.

5. Case 2) No Solution Case Solve the triangle with a = 15 m, b = 25 m and A = 85°

6. Case 3) Two Solution Case Solve the triangle with a = 12 yd., b = 31 yd. and A = 20.5°

7. Area of an Oblique Triangle

8. Find the area of the following figures:

9. 1) Find the area of the shaded region. 2) Find a realistic domain for 3) Find the value of that makes this area of the shaded region a maximum.