Solution to Chapter 2 Problems

 

1)   {a2 = b2+c2} ;  {a2 = (5m)2+(3m)2 = 34m2 } ; {a =√(34m2) = 5.83m}

     {tanB = 5m/3m = 5/3} ; {B = tan-1(5/3) = 59.0}.

     {C = 90 - B = 31.0}.

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2)    a2 = b2+c2 ;  (9m)2 = (7m)2+ c2 ; {c =√(32m2) = 5.66m}

       cosC = 7m/9m = 7/9 ; {C = cos-1(7/9) = 38.9}.

     {B = 90 - C = 51.1}.

 

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3)                       {B = 90 - 58 = 32}.

      sin58 = 8m/a ;  {a = 8m/(sin58) = 9.43m}.

      tanB = b/8m   ;  {b = (8m)tan32 = 5.00m}.

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4)   a2 = b2+c2 ;  a2 =(8m)2+(8m)2 =34m2  ; {a =√(128m2) = 11.3m}

                                tanB = 8m/8m = 5/3 ; {B = tan-1(8/8) = 45.0}.

                                                       {C = 90 - 45 = 45}.

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5)   sin28 = c/5m  ;   {c = (5m)sin28 = 2.35m}.

                           {B = 90 - 28 = 62}.

       sinB = b/(5m)  ;  {b = (5m)sin62 = 4.41m}.

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6) {C = 90 - 55 = 35}.

     sinC = c/7m ;  {c = 7m(sin35) = 4.02m}.

     sinB = b/7m ;  {b = 7m(sin55) = 5.73m}.

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7)                       {C = 90 - 55 = 35}.

     tan55 = b/1m  ; {b = (1m)tan55 = 1.43m}.

     cos55 = 1m/a  ; {a = (1m)/cos55 = 1.74m}.

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 9) To be done by students.