0e5c143f3bb0f0b45bb2bebd7d8046ee.ppt
- Количество слайдов: 18
6 -2: The Law of Cosines Objectives: • Derive The Law of Cosines • Solve triangles using The Law of Cosines © 2002 Roy L. Gover (www. mrgover. com)
Try This in S s e You are building a house. f o The roof has the dimensions w a the L in the diagram. h Find width of the wit lower beam. n o ti u l o N S 60’ 100° o w 90’
Important Idea Law of Sines cannot be used if: • 2 sides and the included angle are given (SAS) • 3 sides and no angles are given (SSS)
Analysis A c B b h a-x a x C
A c B a-x h a b x C
A c B a-x h a b x C
A c B a-x h a b aka the x C Law of Cosines
Example You are building a house. The roof has the dimensions in the diagram. Find the width of the lower beam. 60’ 100° w 90’
Example 60’ 100° w 90’
Definition The Law of Cosines in 3 parts: Do you see a pattern?
Example Solve triangle ABC (find the missing sides & angles) if A=39. 4°, b=12 & c=14
Example Solve triangle PQR if p=14, q=15 & r=16.
Try This Solve triangle ABC if a= 19, b=24. 3 & c =21. 8. Round angle measures to the nearest tenth. B A=48. 3° 21. 8 19 B=72. 7° A 24. 3 C C=59. 0°
Try This Solve triangle ABC if a= 4, b= & C= rads. All answers should be exact values. B A= rad 4 2 B= rad A C c=2
Example • Natalie is flying from Dallas to Little Rock, a distance of 319 miles. She starts her flight radians off course and flies for 75 miles. How far is she from Little Rock?
75 319 i. m mi d
Lesson Close The Law of Cosines is used to solve triangles when: • Two sides and an included angle are known • Three sides are known
Assignment Page 441 #3, 5, 11 -21 odd
0e5c143f3bb0f0b45bb2bebd7d8046ee.ppt