1. Law of Cosines Lesson 4.2

2. 2 Who's Law Is It, Anyway?  Murphy's Law: Anything that can possibly go wrong, will go wrong (at the worst possible moment).  Cole's Law ?? Finely chopped cabbage

3. 3 Solving an SAS Triangle  The Law of Sines was good for ASA- two angles and the included side AAS- two angles and any side SSA- two sides and an opposite angle (being aware of possible ambiguity)  Why would the Law of Sines not work for an SAS triangle? 15 12.5 26° No side opposite from any angle to get the ratio

4. 4 Deriving the Law of Cosines  Write an equation using Pythagorean theorem for shaded triangle. b h a k c - k A B C c

5. 5 Law of Cosines  Similarly  Note the pattern

6. 6 Applying the Cosine Law  Now use it to solve the triangle we started with  Label sides and angles Side c first 15 12.5 26° A B C c

7. 7 Applying the Cosine Law  Now calculate the angles use and solve for B 15 12.5 26° A B C c = 6.65

8. 8 Applying the Cosine Law  The remaining angle determined by subtraction 180 – 93.75 – 26 = 60.25 15 12.5 26° A B C c = 6.65 Experiment with Cosine Law Spreadsheet Experiment with Cosine Law Spreadsheet

9. 9 Wing Span  The leading edge of each wing of the B-2 Stealth Bomber measures 105.6 feet in length. The angle between the wing's leading edges is 109.05°. What is the wing span (the distance from A to C)?  Hint … use the law of cosines! A C

10. 10 Assignment A  Lesson 4.2A  Page 308  Exercises 1 – 27 odd, and 41 - 51 odd

11. 11 Using the Cosine Law to Find Area  Recall that  We can use the value for h to determine the area b h a A B c C

12. 12 Using the Cosine Law to Find Area  We can find the area knowing two sides and the included angle  Note the pattern b a A B c C

13. 13 Try It Out  Determine the area of these triangles 127° 12 24 76.3° 42.8° 17.9

14. 14 Cost of a Lot  An industrial piece of real estate is priced at $4.15 per square foot. Find, to the nearest $1000, the cost of a triangular lot measuring 324 feet by 516 feet by 412 feet. 516 412 324

15. 15 Assignment B  Lesson 4.2B  Page 309  Exercises 29 – 39 odd and 53 – 61 odd