SOLUTION: Please help me find the sides of a, b, and c of the triangle that is a = 4 , b = 8, c = 10 So far I have {{{ 2^2 + 4^2 -2 *4*cos(c)=5^2 }}} {{{ -16cos(c)=25-4-16 }}} {{{ -16cos(c

Algebra ->  Test -> SOLUTION: Please help me find the sides of a, b, and c of the triangle that is a = 4 , b = 8, c = 10 So far I have {{{ 2^2 + 4^2 -2 *4*cos(c)=5^2 }}} {{{ -16cos(c)=25-4-16 }}} {{{ -16cos(c      Log On


   

Question 1077542: Please help me find the sides of a, b, and c of the triangle that is a = 4 , b = 8, c = 10
So far I have +2%5E2+%2B+4%5E2+-2+%2A4%2Acos%28c%29=5%5E2+
+-16cos%28c%29=25-4-16+ +-16cos%28c%29=5+
+cos%28c%29+=+-5%2F16+ +c+=+180-71.79+ +c+=+108.21+%2A+degrees+
Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me find the sides of a, b, and c of the triangle that is a = 4 , b = 8, c = 10
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You mean find the angles.
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So far I have +2%5E2+%2B+4%5E2+-2+%2A4%2Acos%28c%29=5%5E2+
20 - 8cos(C) = 25
Not -16cos, -8
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********** +-16cos%28c%29=25-4-16+ +-16cos%28c%29=5+
+cos%28c%29+=+-5%2F8+ +c+=+180-71.79+ +c+=+108.21+%2A+degrees+
C =~ 128.68 degs
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I would use the Law of Sines to find a 2nd angle.
sin(C)/c = sin(A)/a
sin(A) = a*sin(C)/c = 4*0.7806/10 = 0.31225
A = 18.195 deg
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B = 180 - (A + C)

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
c^2=a^2+b^2-2ab cos C
10^2=4^2+8^2-2(32) cos C
100=80-64 cos C
20=-64 cos C
-5/16=cos C, as you got, which is 108.21 deg.
Now use Law of Sines
4/sin A=10/sin 108.21=10.527
sin A=4/10.527=22.33 degrees
B should be 49.46 deg
8/sin B=10.527; sin B=8/10.527=0.7600, which it is.
A=22.33 deg
B=49.46 deg
C=108.21 deg