In triangle ABC, a=22 cm, c=24.1 cm, and measure of angle A=58 degrees. Determine a possible measure of angle C.

A)21.72 B)53.72 C)111.72 D)none of the above

I keep getting 68.3 as my answer for the measure of angle C therefore I choose none of the above, but my teacher marked it wrong so I was confused. Any help?

Question

In triangle ABC, a=22 cm, c=24.1 cm, and measure of angle A=58 degrees. Determine a possible measure of angle C. 

A)21.72     B)53.72     C)111.72      D)none of the above 

I keep getting 68.3 as my answer for the measure of angle C therefore I choose none of the above, but my teacher marked it wrong so I was confused. Any help?

anonymous · Answer

is this a law of sines problem?

superhelp101 · Answer

yes

anonymous · Answer

then this represents the "ambiguous case" where there are two possible answers
the one you got taking arcsine, which i guess is $68.3$ and the other $180-68.3$

superhelp101 · Answer

how do I find the other angle ?

anonymous · Answer

i wrote it above

superhelp101 · Answer

would I always subtract 180 from it

anonymous · Answer

yes 
your calculator will only give an angle less than 90 degrees because arcsine is a well defined function
but there could be another one

superhelp101 · Answer

ohhh,thank you, so its C

anonymous · Answer

yes, 
draw tool is not working, so i  cannot make a picture for you 
try drawing it yourself and see that there can be two triangles

superhelp101 · Answer

okay!