Solve the triangle if possible C 61 degree a 47 c 100 Sel

Solve the triangle, if possible C = 61 degree a = 47 c = 100 Select the correct choice below and fill in the answer boxes within the choice. (Round to one decimal place as needed.) A. There is only 1 possible solution for the triangle. The measurements for the remaining angles A and Band side b are as follows: A = degree B = degree The length of side b = B. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side b are as follows. A = degree B = degree The length of side b = The measurements for the solution with the shorter side b are as follows. A = degree B = degree The length of side b = There are no possible solutions for the triangle.

Solution

C = 61 deg ; c = 100 ; a = 47

Use sine law : c/sinC = a/sinA

sinA = a*sinC/c = 47*sin61/100 = 0.411

A 1 = 24.27 deg ; A2 = 180 - 24.27 = 155.73 deg

B1 = 180 -A1 - C = 94.73 ; B2 = 180 - A2 - C = -36.73 deg ( Not possible)

So, only 1 triangle : A1 = 24.27 deg ; B1 = 94.73 deg

b/sinB = c/SinC

b = sin94.73*100/sin61 = 113.95

A = 24.3 deg ; B = 94.7 deg ; b = 114