If the length of side a is 12 centimeters, m
∠b
= 36°, and m
∠c
= 75°, what is the length of side b? round your response to two decimal places.

  b = 7.56 cm  .


All angles in a triangle add up to 180 ;

so m∠A = 180 - (75 + 36) = 180 - 111 = 69 ;

Note:  The law of sines:

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

We have solved for m∠A ; which is:  69;

(sin A) / a = (sin B) / b ;  solve for "b" ;

(sin A) / a = (sin 69) / 12 cm  ;

(sin B) / b = (sin 36) / b ;  solve for "b" .

(sin 69) / 12 cm = (sin 36) / b ; solve for "b" ;

b sin 69 = 12 sin 36 ; 

Divide each side of the equation by "sin 69" ; to isolate "b" on one side of the equation; and to solve for "b" ;


    {b sin 69} / sin 69 = {12 sin 36} / sin 69 ;

            b =  (12 sin 36) / sin 69 = 7.5552387639166787

   b = 7.56 cm .