Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14 An explanation would be gravely appreciated.

Answer:First triangle[tex]B=67.4\°[/tex][tex]C=53.6\°[/tex][tex]c=12.2\ units[/tex]Second triangle[tex]B=112.6\°[/tex][tex]C=8.4\°[/tex][tex]c=2.2\ units[/tex]Step-by-step explanation:In this problem we have[tex]A=59\°[/tex][tex]a=13\ units[/tex][tex]b=14\ units[/tex]First TriangleStep 1Find the value of angle BApplying the law of sines[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}[/tex]substitute and solve for B[tex]\frac{13}{sin(59\°)} =\frac{14}{sin(B)}\\ \\sin(B)=14*sin( 59\°)/13\\ \\sin(B)=0.9231\\ \\B=arcsin(0.9231)\\ \\B=67.4\°[/tex]There are two measures of angle B, supplementary to each otherStep 2Find the value of angle CRemember thatthe sum of the internal angles of a triangle is equal to [tex]180\°[/tex]so[tex]A+B+C=180\°[/tex]we have[tex]A=59\°[/tex][tex]B=67.4\°[/tex]substitute and solve for C[tex]59\°+67.4\°+C=180\°[/tex][tex]C=180\°-(59\°+67.4\°)=53.6\°[/tex]Step 3Find the measure of side cApplying the law of sines[tex]\frac{a}{sin(A)} =\frac{c}{sin(C)}[/tex]substitute and solve for c[tex]\frac{13}{sin(59\°)} =\frac{c}{sin(53.6\°)}[/tex][tex]c=\frac{13}{sin(59\°)}*sin(53.6\°)\\\\c=12.2\ units[/tex]Second TriangleStep 1Find the value of angle BApplying the law of sines[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}[/tex]substitute and solve for B[tex]\frac{13}{sin(59\°)} =\frac{14}{sin(B)}\\ \\sin(B)=14*sin( 59\°)/13\\ \\sin(B)=0.9231\\ \\B=arcsin(0.9231)\\ \\B=67.4\°[/tex]Remember that the angle B can take two values [tex]B=180\°-67.4\°=112.6\°[/tex]Step 2Find the value of angle CRemember thatthe sum of the internal angles of a triangle is equal to [tex]180\°[/tex]so[tex]A+B+C=180\°[/tex]we have[tex]A=59\°[/tex][tex]B=112.6\°[/tex]substitute and solve for C[tex]59\°+112.6\°+C=180\°[/tex][tex]C=180\°-(59\°+112.6\°)=8.4\°[/tex]Step 3Find the measure of side cApplying the law of sines[tex]\frac{a}{sin(A)} =\frac{c}{sin(C)}[/tex]substitute and solve for c[tex]\frac{13}{sin(59\°)} =\frac{c}{sin(8.4\°)}[/tex][tex]c=\frac{13}{sin(59\°)}*sin(8.4\°)\\\\c=2.2\ units[/tex]