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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.

Respuesta :

antonsandiego
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:C

Step-by-step explanation:

there are two triangles as

[tex]A=30^{\circ}[/tex]

a=2

b=3

Using sine rule

[tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex]

[tex]sinB=sinA\times \frac{b}{a}[/tex]

sinB=0.75

[tex]B=48.59^{\circ}[/tex]

[tex]\pi -B=48.59^{\circ}[/tex]

B=131.41

For these two values two values of C is possible

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