1. Trigonometry January 6, 2015

2. Section 8.1 ›In the previous chapters you have looked at solving right triangles. ›For this section you will solve oblique triangles- triangles with no right angle. ›As a standard of notation, the angles of the triangle will be labeled A, B, and C and the opposite sides of the triangle will be labeled a, b, and c. a c b A B C

3. Solving an oblique triangle ›To solve an oblique triangle you need to know the measure of at least one side and any two other parts of the triangle. –Two angles and one side (AAS or ASA) –Two sides and an angle opposite (SSA) –Three sides (SSS) –Two sides and their included angle (SAS)

4. Law of Sines and the Law of Cosines ›The first two of these scenarios can be solved using the Law of Sines. ›The second two can be solved using the Law of Cosines (which we will get to later)

5. Law of Sines ABC is Acute ABC is Obtuse

6. Law of Sines

7. The Ambiguous Case (SSA) ›You will see that two angles and one side determine a unique triangle. However, if two side and one opposite angle are given, three possible situations can occur: –(1) no such triangle exists –(2) one such triangle exists –(3) two distinct triangles may satisfy the conditions ›Please refer to and copy the blue box on page 584 of your book

8. Area of an Oblique Triangle

10. Examples…. ›Take the opportunity to work through the examples given in the section (there are 7 examples) ›Do this in detail- go through them step by step and figure out (read) how/why each step was done ›When this is complete move onto the assignment

11. Assignment Page 588 #1-4, #5-8, #13-14, #17-18, #19-26, #27-30, #31-32, #37-44 GRADED PORTION: #2, #6, #14, #26, #32, #40, #42 DUE DATE: TBD