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

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



Answer by Edwin McCravy(20055)   (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



 = sin(42°)
 = sin(42°)
AD = 10·sin(42°)
AD = 6.69

 = sin(32°)
 = sin(32°)
AC·sin(32°) = 6.69
AC = 
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
RELATED QUESTIONS

How do you determine a right triangle using the pythagorean... (answered by Alan3354)
How do you find the perimeter of triangle ABC on the Pythagorean... (answered by ewatrrr)
I'm trying to find the length of a leg on a right triangle. One leg is 52 and the... (answered by ohtheirony)
How do you find the value of different sides using the Pythagorean theorem? Also, please... (answered by Alan3354)
Using the pythagorean Theorem, find the hypotenuse of a right triangle whose legs are 8... (answered by prateekagrawal)
how do you do the pythagorean... (answered by Alan3354)
How do I Determine which of the following side lengths for triangle ABC would form a... (answered by ikleyn)
how do you solve the pythagorean... (answered by apachemexican1)
how do you use the pythagorean theorem to find the lengths of the sides of a triangle... (answered by josgarithmetic)