Posted by Samantha on .
How do you solve a triangle with two solutions? The problem says that A=40 degrees, b=10, and a=14. So I did this:
14>(10)(sin 40)
And this means that there are two solutions according to the equations my teacher gave me.
What do I do now?

Algebra II 
Reiny,
by Sine Law :
sinB/b = sinA/a
sinB/10 = sin40/14
sinB = .459134
angle B = 27.33º or 18027.33º
so B is either 27.33 or 152.67º
draw the two possible triangles, and use the sine law again to find c. 
Algebra II 
Samantha,
Oh, I see. So there would be two solutions for both B and C. I would just solve it like a regular triangle, and B' and C' would be 180 minus the values of B and C. Thanks!

Algebra II 
Reiny,
You got it !!