Question

State whether the given measurements determine zero, one, or two triangles. A = 80°, a = 24, b = 50

Answer 1

The answer you are looking for here is zero. Enjoy!

Answer 2

We know that
applying the law of sines
a/sin A=b/sin B---------> a*sin B=b*sin A
A = 80°, a = 24, b = 50
sin B=[b*sin A]/a-----> sin B=50*sin 80/24-----> sin B=2.0517

the sines value can not be greater than 1
hence

the answer is
zero triangles