se the Law of Sines to solve if possible the triangle If two

se the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.)

A = 55°,  a = 9.1,  b = 10.1

Case 1:

B=65.39 B=

C=59.61 C=

c=9.58 c=

Solution

absinC = bcsinA

c/sinC = a/sinA = b/sinB

=>. sinB = bsinA/a = (10.1sin55)/9.1 = 0.909

=> B = 65.39

=> C = 180 - 55 - 65.39 = 59.61

=> c = 9.1 x sin59.61/sin55 = 9.58

also   sinB = bsinA/a = (10.1sin55)/9.1 = 0.909

=> B = 114.61

=> C = 180 - 55 - 114.61 = 10.39

=> c = 9.1sin10.39/sin55 = 2.003