SOLUTION: how do you find the perimeter of a non right triangle using the pythagorean theorem

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Question 697680: how do you find the perimeter of a non right triangle using the pythagorean theorem



Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose you know one side and two angles, say,
AB = 10, Angle B = 42°, Angle C = 32° 



Draw perpendicular AD from A to BC



AD%2FAB = sin(42°)
AD%2F10 = sin(42°)
AD = 10·sin(42°)
AD = 6.69

AD%2FAC = sin(32°)
6.69%2FAC = sin(32°)
AC·sin(32°) = 6.69
AC = 6.69%2Fsin%28%2232%B0%22%29
AC = 12.62

Use the Pythagorean theorem to find BD

BD˛ + AD˛ = AB˛
      BD˛ = AB˛ - AD˛
      BD˛ = 10˛ - 6.69˛
      BD˛ = 55.2439
      BD = √55.2439
      BD = 7.43

Use the Pythagorean theorem to find DC

DC˛ + AD˛ = AC˛
      DC˛ = AC˛ - AD˛
      DC˛ = (12.62)˛ - (6.69)˛
      DC˛ = 114.5083
       DC = √114.5083
       DC = 10.70

We have side AB = 10, side AC = 12.63, and since we have
BD = 7.43 and DC = 10.70, we have side BC = BD+DC = 7.43+10.70 = 18.13

So we can find the perimeter AB + BC + AC = 10 + 18.13 + 12.62 = 40.75

Edwin