1. Law of Sines, (Because not all triangles are right.)

2. Oblique Triangle vs Right Triangle A B C c a b Look, NO RIGHT ANGLE !

3. Oblique vs Right Triangle A B C c a b a = c sin(A) b = c sin(B)

4. Oblique Triangles have three Altitudes (heights.)

5. Heights can fall outside of an oblique triangle. for

6. Consider an Oblique Triangle and two of its altitudes:

9. The Law of Sines:

10. When a height is outside of the triangle the Law of Sines works the same.

11. In Certain Cases 3 Values Can Identify One, Unique Triangle We need three measures to find a fourth in the proportion... Mathematically we can have: All Angles2 Angles, 1 Side1 Angle, 2 SidesAll Sides AAAAASASSSSS ASASAS SAASSA S A A A SS S S S A SS A A S S ?

12. Necessary Information for Law of Sines

13. Solving Triangles Using Law of Sines Minimum Information: Know 2 angles & 1 side opposite an angle. Know 2 sides & 1 opposing angle. How to solve: Write Proportions. Use cross products. Find all missing angles and side lengths.

14. Applications are Everywhere A balloon is in the air, and we want to find out its height. We know this:

15. Applications are Everywhere #63 On the board...

16. Necessary Information for Law of Sines Be very careful with SSA. It works, if YOU work it. Page 625

17. Draw and check for SSA for every problem. = h b > a > h < h b a a > b A

18. Area A = (1/2)bh where b is base and h is height Using trig, h = a sin(C) QED: A = (1/2)ab sin(C) similarly (argh!) A = (1/2)bc sin(A) A = (1/2)ac sin(B)

19. Find the Area A = 40, b = 52, and <C = 42 o

20. Example 4 in your book How interesting… Can we reproduce this? Grants Pass is at 123.3284 o W...

21. Call a Friend? Extra credit : Find someone whose longitude is close to 132.33 o W, and arrange to find the angle of inclination to the moon at a specific time on the same day. Calculate the distance to the moon using your results.

22. Call a Friend? Extra credit : Find someone whose longitude is close to 132.33 o W, and arrange to find the angle of inclination to the moon at a specific time on the same day. Calculate the distance to the moon using your results.

23. Call a Friend? Extra credit : Find someone whose longitude is close to 132.33 o W, and arrange to find the angle of inclination to the moon at a specific time on the same day. Calculate the distance to the moon using your results.