Posted by DW on Sunday, April 7, 2013 at 11:25am.
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

PreCalculus  Reiny, Sunday, April 7, 2013 at 11:35am
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.

PreCalculus  DW, Sunday, April 7, 2013 at 11:39am
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

PreCalculus  Reiny, Sunday, April 7, 2013 at 12:05pm
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.

PreCalculus  DW, Sunday, April 7, 2013 at 12:09pm
thank you so much!!!
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