In triangle 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?

There are no triangles because b sin A < a.

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

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

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

Question

Kayleigh Oconnor

Mathematics

9 August, 00:24

In triangle 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?

There are no triangles because b sin A < a.

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

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

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

+3

Answers (2)

Know the Answer?

Jada · Answer 1

That person who answered wrong

Terrance · Answer 2

Apply the Law of Sines.

sinB/b = sinA/a

sinB/3 = sin (30°) / 2

sinB = (3/2) sin (30°) = 0.75

Therefore

bsinA = 3*sin (30) = 1.5

0.5b = 0.5*3 = 1.5

Answer:

There is exactly one triangle because b sinA = 0.5b.