Solve the triangle ABC if the triangle exists B 30 degree 4

Solve the triangle ABC, if the triangle exists. B = 30 degree 42\' a = 39.4 b = 28.3 Select the correct choice below and fill in the answer boxes within the choice. A. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side c are as follows. m A = degree m C = degree The length of side c = The measurements for the solution with the shorter side c are as follows. m A = degree m C = degree The length of side c = B. 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 = degree m C = degree The length of side c = c. There are no possible solutions for this triangle.

Solution

B= 30degrees 42 minutes, = 30.7 a = 39.4 ; b = 28.3

apply sine ruls : b/sinB = a/sinA

a/sinA = b/sinB

sinA = a*sinB/b = 39.4*sin30.7/28.3

A1 = 45.3 deg , A2 = 134.7 deg = 134deg42min

C1 = 180-45.3 - 30.7 = 104 deg

C2 = 14.6 deg = 14deg 36 min

c/sinC = b/sinB

c1 = sinC1b/sinB = 74.88

; c2 = sinC2*b/sinB = 19.45

Option A