1. Law of Sines Lesson 6.1

2. 2 Working with Non-right Triangles  We wish to solve triangles which are not right triangles B A C a c b h

3. 3 Using the Sine Law  If we know two angles and one side, we can solve the triangle Actually, if we know two angles, we know all three B A =23.5° C = 112° a c b = 216.75

4. 4 Using the Sine Law  If we know two sides and an opposite angle We can solve the whole triangle  Now how to find angle C and then side c? A C a =9.5 c b=15 B = 47°

5. 5 The Ambiguous Case (SSA)  Given two sides and an angle opposite one of them, several possibilities exist No solution, side too short to make a triangle One solution, side equals altitude 20° 10 1 20° 10 3.42

6. 6 The Ambiguous Case (SSA) Two possible triangle could result (why?) One unique solution, the opposite side is longer than adjacent side 20° 10 5 A A' Solving for A could give either an acute or obtuse angle! 20° 10 13.42

7. 7 Try It Out  Solve these triangles – watch for ambiguous case 28° 78° 44 32° 9.0 14

8. 8 Height of a Kite  Two observers directly under the string and 30' from each other observe a kite at an angle of 62° and 78°. How high is the kite? 30 78° 62° ?