[Note: I've attempted these problems 4 times and I haven't been able to get any of them correct. I really need help with this, please.]

Question

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠A1 is smaller than ∠A2.)

b = 25, c = 38, ∠B = 28°

1). ∠A1= _______° degrees
2). ∠A2= _______° degrees
3). ∠C1= _______° degrees
4). ∠C2= _______° degrees
5). a1 = _______
6). a2 = _______

Answer 1

Assuming you are following the convention that
a is opposite angle A, etc

Sin C/38 = sin28/25

sinC = .71359..
angle C = appr45.5°
then angle A = 180-28-45.5 = 106.5°

second case:
C = 180-45.5 = 134.5°
then angle A = 180 - 28 - 134.5 = 17.5°

I will leave it up to you to find sides a for each case

You are dealing with the "ambigious case" here.

Answer 2

So what is ∠C2?
I'm confused

Answer 3

Angel c2 is the 2nd angle due to the ambigious case. So it would be 17.5 degrees and angle c1 would be 106.5 degrees

Hope that helps!