solve each triangle using the Law of Sines If there is no so

solve each triangle using the Law of Sines. If there is no solution, write “no solution.” Round each answer to the nearest tenth.

A = 76°, a = 15, b = 5

A = 97.5°, a = 13, b = 9

1) A = 76°, a = 15, b = 5

Apply sine rule:

a/sinA = b/sinB

sinB = 5*sin76/15 =0.3234

B1 = 18.87 deg

B2 = 180 -18.87 = 161.13 deg

A2 +B2 > 180

So, only triangle possible:

C = 180 -76 - 18.87 = 85.13 deg

c/sinC = a/sinA

c = sin85.13*15/sin76 = 15.40

2) A = 97.5°, a = 13, b = 9

a/sinA = b/sinB

sinB =0.686

B = 43.34 deg

C = 180 -97.5 - 43.34 = 39.16 deg

c/sinC = a/sinA

c =sin39.16*13/sin97.5 = 8.28