Solve ΔABC. (Round your answers for b to one decimal place. Round your answers for 𝛽 and 𝛾 to the nearest 10 minutes. If there is no solution, enter NO SOLUTION.)

Question

Solve ΔABC. (Round your answers for b to one decimal place. Round your answers for 𝛽 and 𝛾 to the nearest 10 minutes. If there is no solution, enter NO SOLUTION.)

𝛼 = 24°30',    c = 55.3,    a = 37.4

smaller b:

b =
𝛽 =	°  '
𝛾 =	°  '

larger b:

b =
𝛽 =	°  '
𝛾 =	°  '

Answer 1

sinA/a = sinC/c =

sin24.5/37.4= sinC/55.337

.4147/37.4 = .0111 = sinC/55.3

sinC = 55.3(.0111) = 0.61312

C = 37.819 degrees or 180-37.819 = 142.181 degrees but ignore the 2nd solution for C as it sums to more than 180 when added to 55.3

A= 24.5, C = 37.8, B = 180-24.5-37.8 = 117.7 degrees

sinB/b = .0111

sin117.7 = 0.8854

0.8854/b = 0.0111

b = .8854/.0111 = 79.8