Respuesta :

Using the sine rule; a/sin A=b/sin B=c/sin C , where a,b and c are the edges and A,B and C are the angles of the triangle.
Thus, in this case 19/sin 32= 12/ sin B
                                          B = 19.55°

 Angles in a triangle add up to 180, thus 
                                                C = 180- (32+19.55)
                                                 C = 128.45 °
 From the sine rule we can determine c
 a/ sin A= c/sin C
     19/ sin 32 = c /sin 128.45
                   c = 29.08
Yna9141
If we are told to solve the triangle, this usually means that we have to determine everything about it (all angles and sides). Using the sine Law, we can determine the measure of angle B.

                       a/sin A = b/sin B
Substituting the known values,
                19 / sin (32) = 12 / sin B
The value of B from the equation is 19.55°.

Then, we can solve for the measure of angle C by subtracting the sum of measures of angle A and B from 180.

                 C = 180 - (32° + 19.55°)
                  C = 128.45°

Then, determine the length of side C by using again the sine law.

                      19/sin (32) = c/ sin(128.45)
                        c = 29.08 

Thus, the sides are a = 19, b = 12, and c = 29.08 and the angles are A = 32°, B = 19.55°, and C = 128.45°. 

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