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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.

User Jambaaz
by
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2 Answers

4 votes

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

User Basit
by
8.5k points
5 votes
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.
User Parth Pitroda
by
7.2k points

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