SOLUTION: In a triangle abc, |ac|=8cm, |ab|=10, Area=20cm^2. Find possible values for <bac Thank you

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Question 397894: In a triangle abc, |ac|=8cm, |ab|=10, Area=20cm^2. Find possible values for
Thank you
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
Area S=1/2*|ab|*|ac|*sina
20=1/2*10*8*sina
sina=1/2
a=30 degrees
Cosines theorem |bc|^2=|ab|^2+|ac|^2-2*|ab|*|ac|*cosa
|bc|^2=100+64-2*10*8*cos30=164-80sqrt(3)=25.43
|bc|=5.04
sinus theorem %28ab%29%2Fsinc=%28ac%29%2Fsinb=%28bc%29%2Fsina
10%2Fsinc=5.04%2Fsin30; sinc=%2810%2Asin30%29%2F5.04=0.99
c = 82 degrees
a+b+c=180 degrees
b=180-82-30=68 degrees