SOLUTION: Find the length x in the triangle. Side 1=8. Side 2=x. Side 3=12

Algebra ->  Algebra  -> Triangles -> SOLUTION: Find the length x in the triangle. Side 1=8. Side 2=x. Side 3=12      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 118094: Find the length x in the triangle. Side 1=8. Side 2=x. Side 3=12
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the triangle is a right triangle and that side 3 is the hypotenuse.


We basically have this triangle set up:

drawing%28500%2C500%2C-0.5%2C2%2C-0.5%2C3.2%2C%0D%0A%0D%0Aline%280%2C0%2C0%2C3%29%2C%0D%0Aline%280%2C3%2C2%2C0%29%2C%0D%0Aline%282%2C0%2C0%2C0%29%2C%0D%0Alocate%28-0.2%2C1.5%2C8%29%2C%0D%0Alocate%281%2C-0.2%2Cx%29%2C%0D%0Alocate%281%2C2%2C12%29%0D%0A%29
Since we can see that the triangle has legs of 8 and x with a hypotenuse of 12, we can use Pythagoreans theorem to find the unknown side.


Pythagoreans theorem:

a%5E2%2Bb%5E2=c%5E2 where a and b are the legs of the triangle and c is the hypotenuse



8%5E2%2Bx%5E2=12%5E2 Plug in a=8, b=x, and c=12. Now lets solve for x


6+4+%2B++x++%5E+2+=+1+4+4 Square each individual term



+x++%5E+2+=+1+4+4+-+6+4 Subtract 64 from both sides


+x++%5E+2+=+8+0 Combine like terms


s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+8+0+%29 Take the square root of both sides


x=4%2Asqrt%285%29 Simplify the square root


Which approximates to...
x+=+8+.+9+4+4+2+7+1+9+0+9+9+9+9+1+6

So our answer is
x+=+8+.+9+4+4+2+7+1+9+0+9+9+9+9+1+6