1. 6.1 Law of Sines +Be able to apply law of sines to find missing sides and angles +Be able to determine ambiguous cases

2. Oblique Triangles A is acute A is obtuse A a B b C c A B C a b c

3. Solving Oblique Triangles To solve oblique triangles you need one of the following cases 2 angles and any side (AAS or ASA) 2 sides and the angle opposite one of them (SSA) 3 sides (SSS) 2 sides and their included angle (SAS)

4. Law of Sines If ABC is a triangle with sides a, b, and c, then

5. Example Find the missing sides and angles given the following information C = 102.3 0 B = 28.7 0 b = 27.4 ft

6. Word Problem A pole tilts towards the sun at an 8 0 angle from the vertical, and it casts a 22 foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is 43 0. How tall is the pole?

7. Ambiguous Cases (SSA) (h = bsinA) A is acute a < h no triangles A is acute a = h 1 triangle A a h b A b ah

8. More Cases A is acute a > b 1 triangle A is acute h < a < b 2 triangles A ba h A b ha a

9. More Cases A is obtuse a < b no triangles A is obtuse a > b 1 triangle A a b A b a

10. Example Find the missing sides and angles of the triangle given the following information a = 22 in b = 12 in A = 42 0

11. Determine how many triangles there would be? 1)A = 62 0, a = 10, b = 12 2)A = 98 0, a = 10, b = 3 3)A = 54 0, a = 7, b = 10

12. Finding two solutions Find two triangles for which a = 12, b = 31, and A = 20.5 0

13. Example Find the missing sides and angles for the following information a = 29 b = 46 A = 31 0

14. Using Sine To Find Area Area of an Oblique Triangle

15. Find the Area of the Triangle Find the area of a triangular lot having two sides of lengths 90 meters and 52 meters and an included angle of 102 o.

16. Word Problem The course for a boat race starts at point A and proceeds in the direction S 52 o W to point B, then in the direction S 40 o E to point C, and finally back to point A. Point C lies 8 kilometers directly south of point A. Approximate the total distance of the race course.