SOLUTION: Find the length x in the triangle. Express your answer in simplified radical form. Side 1=10. Side 2=8. Side 3=x

Algebra ->  Algebra  -> Triangles -> SOLUTION: Find the length x in the triangle. Express your answer in simplified radical form. Side 1=10. Side 2=8. Side 3=x      Log On

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

   

Question 118091: Find the length x in the triangle. Express your answer in simplified radical form. Side 1=10. Side 2=8. Side 3=x
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%2C10%29%2C%0D%0Alocate%281%2C-0.2%2C8%29%2C%0D%0Alocate%281%2C2%2Cx%29%0D%0A%29
Since we can see that the triangle has legs of 10 and 8 with a hypotenuse of x, 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



10%5E2%2B8%5E2=x%5E2 Plug in a=10, b=8, and c=x. Now lets solve for x


1+0+0+%2B+6+4+=++x++%5E+2 Square each individual term



1+6+4+=++x++%5E+2 Combine like terms


s+q+r+t+%28+1+6+4+%29+=+s+q+r+t+%28++x++%5E+2+%29 Take the square root of both sides


2%2Asqrt%2841%29=x Simplify the square root


Which approximates to...

12.8062484748657=x

So our answer is
x=12.8062484748657