We kmow that #/_B# is #143^o# and #C=20^o#. Since the angles within a triangle must add up to #180^o#. #143+20=163#. #180-163# leaves us with #17^o#. So now we know all the inner angles. We just need to find the lengths.
I'm going to use the law of sines, which says that #sinA/a=SinB/b#. We can also write this as #a/SinA=b/SinB# too since both of these formulas are synonymous. In order to use this formula we need three known variables and one unknown. We know the length of #b# and all the angles, so we should be good.
Let's set this up:
#a/Sin17^o=37/Sin143#
#a/.2923=61.481#
#a=17.9752~~18#
Great job! Let's do the next one!
#c/Sin20^o=37/Sin143^o#
#c/.342=61.481#
#c=21.027~~21#
Okay, we're good! Nice work, we're done. We know all the lengths and all the angles.. Hopes this helps!
