Question

Given m∠B = 81°47′, m∠A = 41°52′, and b = 3,579, find the remaining sides to f angle to the nearest degree.

Answer 1

Given

∠ B = 81 degree 47'

∠ A = 41 degree 52'

b = 3,579

1 degree = 60'

1' = 1 / 60 degrees

47' = 47 / 60 degrees

81 degree 47' = 81 + 47 / 60 degrees = 81.7833 degrees = ∠ B

52' = 52 / 60 degrees

41 degree 52' = 41 + 52 / 60 degrees = 41.8666 degrees = ∠ A

Applying Sine rule

sin( A ) / a = sin( B ) / b

=> sin( 41.8666 ) / a = sin( 81.7833 ) / 3,579

=> 3579*sin( 41.8666 ) / sin( 81.7833 ) = a

=> a = 2413.39 ~ 2413

We know that sum of angles of a triangle

∠ A + ∠ B + ∠ C = 180 degree

=> 41.8666 + 81.7833 + ∠ C = 180

=> ∠ C = 180 - ( 41.8666 + 81.7833 )

=> ∠ C = 180 - 123.6499 = 56.3501 degree

Applying Sine rule

sin( A ) / a = sin( B ) / b

=> sin( 56.3501 ) / c = sin( 81.7833 ) / 3,579

=> 3,579* sin( 56.3501 ) / sin( 81.7833 ) = c

=> 3010.1999 ~ 3010