Solve the triangle ABC, if the triangle exists. B=31 degree 18\’ a = 37.6 b=32.1 Select the correct choice below and fill in the answer boxes within the choice. There is only 1 possible solution for the triangle. The measurements for the remaining angles A and C and side c are as follows. m A= m C = degree \'(Simplify your answer. Round to the nearest degree as needed. Round to the nearest minute as needed.) The length of side c (Round to the nearest tenth as needed.) There are 2 possible solutions for the triangle. The measurements for the solution with the longer side c arc as follows. m A= m C = degree \'(Simplify your answer. Round to the nearest degree as needed. Round to the nearest minute as needed.) The length of side c (Round to the nearest tenth as needed.) There are 2 possible solutions for the triangle. The measurements for the solution with the shorter side c arc as follows. m A= m C = degree \'(Simplify your answer. Round to the nearest degree as needed. Round to the nearest minute as needed.) The length of side c (Round to the nearest tenth as needed.) There are no possible solutions for this triangle.

### Solution

B = 31.18\’ b = 32.1 and a= 37.6

Apply sine rule :

b/sinB = a/sinA ; sinA = a*sinB/b

sinA = (37.6 *sin31.18)/32.1 = 0.608

A = 37.48 . sin is +ve in Ist and IInd quadrant.

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