Question

Solve the triangle. A = 19°, C = 102°, c = 6

answer choices:
B = 31°, a ≈ 18, b ≈ 15.8 X (I know it is not option A)
B = 59°, a ≈ 2, b ≈ 5.3
B = 59°, a ≈ 18, b ≈ 15.8
B = 59°, a ≈ 18, b ≈ 5.3

Answer 1

we know that

Law of sines established
a/sin A=b/sin B=c/sin C

then
a/sin A=c/sin C------------> a=c*sin A/sin C---------> a=6*sin 19/sin 102
a=1.91 units ≈2 units

A+B+C=180°----------> B=180-(A+C)-----> B=1180-(19+102)
B=59°
a/sin A=b/sin B-----------> b=a*sin B/sin A----->2*sin 59/sin 19
b=5.27 units ≈5.3 units

the answer is the option
B = 59°, a ≈ 2, b ≈ 5.3