Question

State whether the given measurements determine zero, one, or two triangles.

B = 81°, b = 26, c = 28
i think its zero, not sure though.

Answer 1

you are correct its zero

by using Law of sines and trying to solve for angle C, you get angle greater than 180 which is impossible for a triangle

Answer 2

or you could use the triangle inequality
|a| + |b| > |c|

where a, b & c are the lengths of the sides of the triangle (or hypothesized triangle)

Answer 3

oops my calculator was in radian mode....actually you get no solution for angle C

Answer 4

take a & b to be the smallest 2 sides and see if you get a true statement when c is the largest side.
if true, then a triangle is possible.
if false, then no triangle is possible