Question

The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.

B = 111°, c = 8, b = 12

Answer 1

options:
C = 38.5°, A = 30.5°, a ≈ 6.5

No triangle is formed.

C = 30.5°, A = 38.5°, a ≈ 6.5

The triangle cannot be solved with the Law of Sines.

Answer 2

@satellite73 can you help me with this?

Answer 3

yeah sure

Answer 4

\[\frac{\sin(111)}{12}=\frac{\sin(C)}{8}\] from the law of sines

Answer 5

this means
\[\sin(C)=\frac{8\sin (111)}{12}\]

Answer 6

ok

Answer 7

if \(\frac{8\sin(111)}{12}\) is bigger than one, there is no solution, because sine is never bigger than one

Answer 8

it isn't.

Answer 9

but really what we want is not
\[\sin(C)\] but rather \(C
\) itself

Answer 10

and so \(C\) is the arcsine of all that mess

Answer 11

i.e.
\[C=\sin^{-1}\left(\frac{8\sin(111)}{12}\right)\]

Answer 12

38.49

Answer 13

=C

Answer 14

if you say so

Answer 15

lol what do you mean by that

Answer 16

i mean i didn't do it, but you are right

Answer 17

http://www.wolframalpha.com/input/?i=arcsin%288sin%28111%29%2F12%29

Answer 18

oh ok thanks :D

Answer 19

yw

Answer 20

So is the 3rd answer choice correct?

Answer 21

C = 38.5°, A = 30.5°, a ≈ 6.5