Solve each triangle If a problem has no solution state NO SO

Solve each triangle. If a problem has no solution, state NO SOLUTION. If a problem involves two traingles, solve both. alpha = 55.7^degree, a = 39.6 ft, b = 42.8 ft

Solution

a = 55.7 deg ; a= 39.6 ft ; b = 42.8 ft

apply sine rule: a/sinA = b/sinB

sinB = b*sinA/a = 42.8*sin55.7/39.6 =0.89

B1 = 63.23 ; B2 = 180 -63.23 =116.77 deg

C1 = 180 -55.7 -63.23 =61.07 deg ; C2 =180 -116.77 - 55.7 = 7.53 deg

there are two triangles possible

c1/sinC1 =39.6/sin55.7

c1/sin61.07 = 39.6/sin55.7

c1 = 41.95ft

c2/sinC2 = a/sinA

c2 =sin7.53*39.6/sin55.7

c2 = 6.28 ft