The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. B = 153°, c = 10, b = 14

Answer:C = 28.2, A = 25.8, a = 6.5See diagram below.==============================================Work Shown:Given info isB = 126 degreesb = 12c = 7Use the Law of Sines to solve for angle Csin(C)/c = sin(B)/bsin(C)/7 = sin(126)/12sin(C)/7 = 0.067418082864579sin(C) = 7*0.067418082864579sin(C) = 0.471926580052053C = arcsin(0.471926580052053) or C = 180-arcsin(0.471926580052053)C = 28.1594278560921 or C = 180-28.1594278560921C = 28.1594278560921 or C = 151.840572143908C = 28.2 or C = 151.8We have two possible angle values for C.-----------------If C = 28.2, then A = 180-B-C = 180-126-28.2 = 25.8If C = 151.8, then A = 180-B-C = 180-126-151.8 = -97.8So it is not possible for C = 151.8 (because it leads to angle A being negative)Therefore, only C = 28.2 is possible. -----------------Use the law of cosines to find the remaining side 'a'a^2 = b^2 + c^2 - 2*b*c*cos(A)a^2 = (12)^2 + (7)^2 - 2*(12)*(7)*cos(25.8)a^2 = 144 + 49 - 168*0.900318771402194a^2 = 144 + 49 - 151.253553595569a^2 = 41.7464464044315a = sqrt(41.7464464044315)a = 6.46114900032738a = 6.5-----------------Only one triangle is possibleThe fully solved triangle has these angles and sides:A = 25.8 (approx)B = 126C = 28.2 (approx)a = 6.5 (approx)b = 12c = 7With stuff in bold representing the terms we solved for previously. Attached below is an image of the fully solved triangle.