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.}.

{C = 90 - B = 31.}.

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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.}.

{B = 90° - C = 51.}.

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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.}.

{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.