Question

Determine the number of triangles that can be formed with the given information.
and if it forms two possible triangles solve all unknown angles and sides

Angle A=116 degrees
a=10
b=11

Answer 1

One.

Assuming you are using the standard notoation that
b is the side opposite angle B etc.

sinB/11 = sin116°/10
sin B = .9886
angle B = appr 81.4° or appr 98.6°
but the latter is not possible since a triangle cannot have 2 obtuse angles

so B = 81.4° is the only angle possible,
thus only one triangle.

I will leave it up to you to find the other angle and side.

Answer 2

but if you add 81.4 (measure of angle B) plus 116 (measure of angle A) you get 197.368 which is over 180 degrees....
so that would make measure of angle C negative which is why I'm confused

Answer 3

Of course you are right, silly of me not to even check for the obvious.
I was too concerned about the two obtuse angles.
c
so....
No such triangle is possible.

Answer 4

thank you so much!!!