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

Answer:C

Explanation:

there are two triangles as

`A=30^(\circ)`

a=2

b=3

Using sine rule

`(a)/(sinA)=(b)/(sinB)`

`sinB=sinA* (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

Answer 2

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.