SOLUTION: Find length x in each triangle. Express your answer in simplified radical form. x/ | /|||8 ----- 5

Algebra ->  Pythagorean-theorem -> SOLUTION: Find length x in each triangle. Express your answer in simplified radical form. x/ | /|||8 ----- 5       Log On


   

Question 109598: Find length x in each triangle. Express your answer in simplified radical form.
x/ |
/|||8
-----
5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We basically have this triangle set up:


Since we can see that the triangle has legs of 5 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



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


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



8+9+=++x++%5E+2 Combine like terms


s+q+r+t+%28+8+9+%29+=+s+q+r+t+%28++x++%5E+2+%29 Take the square root of both sides

x=sqrt%2889%29 Simplify


Which approximates to...

x=9.4339811320566

So our answer is
x=9.4339811320566