1. Demana, Waits, Foley, Kennedy
5.5
The Law of Sines

2. What you’ll learn about
Deriving the Law of Sines
Solving Triangles (AAS, ASA)
The Ambiguous Case (SSA)
Applications
… and why
The Law of Sines is a powerful extension of the triangle
congruence theorems of Euclidean geometry.

3. Review

4. Overview
A triangle can be defined as long as we have three of the six parts and one of the parts is a side.
1) ASA or SAA
2) SSA (two sides and an angle opposite)
3) SAS (two sides and an included angle)
4) SSS
Situations 1 & 2 can be solved using Law of Sines
Situations 3 & 4 can be solved using Law of Cosines

5. Area of any triangle
The area of a triangle with sides of lengths a and b and with an included angle θ is;
A = 1/2 ab sinθ 3 10

6. Create your own
Create as many problems as possible from the figure shown:

7. Law of Sines
***Angles and sides opposite use same letter***

8. Use area to prove Law of Sines

9. Example: Solving a Triangle Given Two Angles and a Side

10. Solution

11. Solution

12. A satellite orbiting the earth passes directly overhead at observation stations in Phoenix and Los Angeles, 340 miles apart. At an instant when the satellite is between these two stations, its angle of elevation is simultaneously observed to be 60 degrees at Phoenix and 75 degrees at Los Angeles. How far is the satellite from Los Angeles?

13. Example: Solving a Triangle Given Two Sides and an Angle (The Ambiguous Case)

14. Solve the triangle

15. Solve triangle ABC, where angle A = 42 degrees and sides a & b are 70 mm & 122 mm respectively

16. Visual of Ambiguous Case

17. 5.5 HW, Page 439
Be able to do 1 – 22;

18. Solution

19. Solution

20. Solution

21. Solution

22. Solution

23. Solution

24. Example: Finding the Height of a Pole
15ft
15º
65º B A C

25. Solution x
15ft
15º
65º B A C