Solve the triangle ABC if the triangle exists A 445 Degree

Solve the triangle ABC, if the triangle exists. A = 44.5 Degree a = 8.9 m b= 10.6 m 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 B and C and side c are as follows m Angle B = m Angle C = The length of side c = There are 2 possible solutions for the triangle. The measurements for the solution with the longer side c are as follows m Angle B = m Angle C = The length of side c = The measurements for the solution with the shorter side c are as follows. m Angle B = m Angle C = The length of side c = There are no possible solutions for this triangle.

Solution

A = 44.5 deg a = 8.9 b = 10.6

applying sine rule:

a/sinA = b/sinB

sinB = sinA*b/a = sin44.5* 10.6/8,9 = 0.835

B1 = 56.60 deg ; B2 = 180 -56.59 =123.40

C1 = 180 -44.5 -56.60 = 78.9 deg ; C2 = 180 -44.5 -123,40 = 12.1 deg

There are two possible solutions

We find c/sinC1 = a/sinA

c = (a/sinA)*sinC1 = 12.46

c = (a/sinA)*sinC2 = 2.66

Solution: Option B: B = 56.6 deg ; C = 78.9 c = 12.50

                             B = 123.4 dg ; C = 12.1 ; c=2.7