Question 927493: Two sides of a triangle measure 80 cm and 64 cm. The area of the triangle is 2,262 cm. Find the third side. Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! Two sides of a triangle measure 80 cm and 64 cm. The area of the triangle is 2,262 cm [sic] it's sq cm. Find the third side.
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Area = b*h/2
b = 80
A = angle between the given sides
h = 64*sin(A)
2262 = 80*64*sin(A)/2 = 2560*sin(A)
sin(A) = 2262/2560 =~ 0.883594
A =~ 62.1 degs
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c = 3rd side
c^2 = a^2 + b^2 - 2abcos(A)
c^2 = 80^2 + 64^2 - 2*80*64*cos(62.1)
c^2 = 6400 + 4096 - 10240*0.468254 = ~5701
c = 75.5
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Check using Heron's Law
s = (80+64+75.5)/2 = 109.75
Area = 2261.89
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It's surprising, I've been doing this stuff for 55 years or so, and never seen a problem like this one.
