Lesson 6.1 Law of Sines

Draw any altitude from a vertex and label it k. Set up equivalent trig equations not involving k, using the fact that k is equal to itself

Use the Law of Sines in oblique triangles (no right angle) The phrase “solve a triangle” means to find all unknown sides or angle. Example 1 Solve the triangle

Special Cases: Cannot use Law of Sines when given SSS, AAA, or SAS So that leaves 3: ASA, AAS, ASS ASA & AAS give unique solutions ASS (or SSA if you prefer) can give 3 possibilities: 1) Single Solution 2) Two Solutions 3) No Solution

Example 2 Solve the triangle A = 60 o, a = 9, c = 10 Example 3 Solve the triangle A = 42 o, a = 22, c = 12

Example 4 Solve the triangle A = 110 o, a = 125, c = solutions: 2 angles solved from equation give 3 angles that add to solution: only 1 of 2 angles solved from equation work No solution: any solved angle does not work or sin (angle) is undefined

Area of Oblique Triangles Use the formula: In the acute triangle below, c is the base and h is the height Problem: h is not given. Solution: Use trigonometry to find write an equation for h. h h

Formulas: Remember… Use all 3 letters 2 little letters (sides), 1 big (angle) Example Find the area of the triangle. Problem Set 6.1