How do you solve the triangle given ∠B = 143°, ∠C = 20°, b = 37?

1 Answer
Rachel · Zor Shekhtman
Aug 4, 2016

#/_ A=17^0#, #a~~18#
#/_ B=143^0#, #b = 37#
#/_ C= 20^0#, #c~~21#

Explanation:

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!

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