Trig triangle question

Question

Determine whether the given measurements determine 0, 1, or 2 possible triangles.

a= 15.5, c= 24.0, C= 36.9 degrees

Answer 1

sin(36.9)=about 0.6

sinC/c=.6/24=.1/4

sinA/a=.1/4=sinA/15.5

sinA=1.55/4=0.3875

sinA=.3875

A=22.8

36.9+22.8=59.7

B=180-59.7=120.3

sinB=0.8634

sinB/b=.1/4 = .8634/b

(1/10)b=4(.8634)=3.4536

b=34.536

Just one triangle possible

sides about 34.5, 15.5 and 24

angles about 120, 23 and 37

That's assuming the A angle is opposite the a side, B opposite the b side and C opposite the c side

Answer 2

It clear that here is one triange, because a < c. So A < C.

Second triangle here impossible, it will contradict with A + B + C = 180°

Answer 3

sin(A)/15.5=sin(36.9°)/24.0

sin(A)=15.5sin(36.9°)/24.0

A=arcsin(15.5sin(36.9°)/24.0)≈22.8° or 180°-22.8°=157.2°