Given triangle ABC, angle A = 120°, a = 8, b = 3; determine angle B to the nearest whole degree.

Question

anonymous · Answer

I know the law of cosines is sinA/a = sinB/b = sinC/c

hartnn · Answer

do u know sine law ?

hartnn · Answer

that was sin law

anonymous · Answer

This is what I have so far..
sin120/8 = sinB/3
3sin120=8sinB
3/8=sinB

I'm lost from there

anonymous · Answer

Woooow. I meant the law of sines not cosines. I'm just having an off day.

hartnn · Answer

use calculator to find arcsin (3/8)

hartnn · Answer

wait sin 120 = ... ?

zarkon · Answer

what is the sine of 120?

anonymous · Answer

Crap. I'll start over & Thanks so much for helping me

anonymous · Answer

Okay, now this is what I have...
sin120/8=sinB/3
0.58/8=sinB/3
0.07=sinB/3
0.21=sinB
sin^-1(0.21) = 12.12 degrees to the nearest whole number is 12. Right?

hartnn · Answer

0.58 ? 
did you use radian mode ?
sin 120 = 0.866

anonymous · Answer

No.. I used degree mode. How do you know when to use each one?

hartnn · Answer

120 means its in degrees only.
radians angle contains $\pi$ in it. 
and sin 120 degrees = 0.866

anonymous · Answer

Ohh. Well thank you! So my final answer should be 17, right?

hartnn · Answer

what u got sin B as ?

anonymous · Answer

17 degrees

hartnn · Answer

why do i get 18.95 :\

anonymous · Answer

I'm not sure... Lol

hartnn · Answer

arcsin 0.324 = 18.95.

anonymous · Answer

Oh I didn't put the 4 on there so that may have been what messed it up