Question

In ABC, you know that a = 2, b = 3 and m A = 30°. Which option below lists the number of triangles and gives the correct explanation?
A. There are no triangles because b sin A < a.

B. There is exactly one triangle because b sin A = 0.5b.

C. There are two triangles because b sin A < a < b.

D. There are three triangles because b sin A = 0.5b and b sin A < a < b.

Answer 1

I think there isn't one triangle at all, there are two of it. So I suggest to choose C. There are two triangles because b sin A < a < b - as it's exactly correct explanation that excepts other options. 

Answer 2

Answer:C

Step-by-step explanation:

there are two triangles as

$A=30^{\circ}$

a=2

b=3

Using sine rule

$\frac{a}{sinA}=\frac{b}{sinB}$

$sinB=sinA\times \frac{b}{a}$

sinB=0.75

$B=48.59^{\circ}$

$\pi -B=48.59^{\circ}$

B=131.41

For these two values two values of C is possible