Question

How many triangles ABC satisfy the following conditions?
A=50°, b = 19 ft, a = 9 ft

Answer 1

Given two sides and a non-included angle is known as the Ambiguous Case.
There may be 0, 1, or 2 triangles formed with such data.
Using the Law of Sines as a beginning point:
9/ sin(50) = 19/sin B
11.749 = 19/sinB
sin B = 19/11.749
sin B = 1.617 which exceeds 1. The largest value of sine is 1.
Therefore, no such triangle exists with this data.

Answer 2

So the answer is 0 or impossible ?

Answer 3

It is impossible to have a triangle with those measurements. So, there are zero such triangles. Use whatever language you use in class.

Answer 4

Okay thanks Directrix :D