Chapter 7 - Pearson

Section 7.3 The Law of Cosines 105a+ b sin A+sin B39. Prove that = .b sin BStart with the law of sines.a sin= b a =b Asin A sin B sin Ba+bSubstitute for a in the expression .bbsinA bsinA+ b + ba+ b sin sin sin B=B =B ⋅b b b sin BbsinA+bsinB b( sin A+sin B)= =bsinB sin Bsin A+sin B=sin Ba-b sin A-sinB40. Prove that =.a+ b sin A+sin BStart with the law of sines.a sin= b a =b Asin A sin B sin BSubstitute for a in the expression a - ba+ b.bsinA bsinA-b-ba- b sin sin sin B=B =B ⋅a+b bsin A bsin A+ b + bsin Bsin B sin BbsinA-bsinB b( sin A-sinB)= =bsin A+ bsin B b( sin A+sin B)sin A-sinB=sin A+sin B41.42.43. (a)é sin AsinB ùA= 5 Rsin ( A+B)êëúû2A=1.12257R(b)28.77 in.25.32 in.44. redSection 7.3 The Law of Cosines1. (a) SAS(b) law of cosines2. (a) SAA(b) law of sines23. (a) SSA(b) law of sines4. (a) ASA(b) law of sines5. (a) ASA(b) law of sines6. (a) SSA(b) law of sines7. (a) SSS(b) law of cosines8. (a) SAS(b) law of cosines9. 510. 711. 12012. 3013. a » 7.0; C » 21.4 ;B = 37.6°14. a » 5.4 B » 40.7 ;C = 78.315. B » 53.1 ;C = 53.1 ; A » 73.7The angles may not sum to 180° due torounding.16. B » 108.2 ;A » 22.3 ;C = 49.5°17. b » 88.18; A » 56.7 ;C = 68.3°18. C » 95.7 ;A » 33.6 ;B = 50.7°19. aa » 2.60 yd; B » 45.1 ;C = 93.520. c » 2.83 in; A » 44.9 ;B = 106.821. c » 6.46 m; A » 53.1 ;B = 81.322. a » 43.7 km; B » 53.2 ;C = 59.523. A » 82 ;B » 37 ;C = 6124. C » 98 ;A » 29 ;B = 5325. C » 10210 ¢ ; B » 3550 ¢ ; A = 4200¢26. C » 10720 ¢ ; B » 3900 ¢ ; A = 3340¢27. C » 8430 ¢ ; B » 4440 ¢ ; A = 5050¢28. B » 8510 ¢ ; C » 4450 ¢ ; A = 5000¢Copyright © 2013 Pearson Education, Inc.