How do you solve the triangle given a=4, b=8, c=5?

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Answer 1 · 2016-11-03T21:51:44

Please read the explanation for the steps leading to the measures the angles, #A = 24°, B = 125°, and C = 31°#

Use the Law of Cosines to find one of the angles (I choose angle B):

#b^2 = a^2 + c^2 - 2(a)(c)cos(B)#

#b^2 - a^2 - c^2 = -2(a)(c)cos(B)#

#cos(B) = (b^2 - a^2 - c^2)/( -2(a)(c))#

#B = cos^-1((b^2 - a^2 - c^2)/( - 2(a)(c)))#

#B = cos^-1((8^2 - 4^2 - 5^2)/( - 2(4)(5)))#

#B ~~ 125°#

Use the Law of Sines to find another angle (I choose angle A):

#sin(A)/a = Sin(B)/b#

#sin(A) = Sin(B)a/b#

#A = sin^-1(Sin(B)b/a)#

#A = sin^-1(Sin(125°)4/8)#

#A ~~ 24°#

Angle C is found by subtracting the angles A and B from 180°:

#C = 180 - 125 - 24#

#C = 31°#