How do you find the missing sides and angles of a non-right triangle, triangle ABC, angle C is 115, side b is 5, side c is 10?

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Answer 1 · 2016-06-28T15:18:38

#a=6.8; hat B=26.95; hat A=38.05#

You can use the Euler (or sinus) theorem:

#a/sin hat A=color (red) (b/sin hat B=c/sin hat C)#

so

#5/sin hat B=10/sin 115#

#sin hat B=5sin115/10#

#sin hat B=sin 115/2=0.45#

so

#hat B=26.95#

and

#hat A=180-(115+26.95)=38.05#

Since

#color(red)(a/sin hat A)=b/sin hat B=color (red) (c/sin hat C)#

#a/sin 38.05=10/sin115#

#a=10sin38.05/(sin115)#

#a=6.8#