What is the value of x?

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x=

a right triangle. the legs are labeled x and six, and the hypotenuse is labeled ten.

We can use the Pythagorean theorum

a^2+b^2=c^2

c^2 is the length of the longest side squared

so 

6^2 + b^2 = 10^2

36+ b^2 = 100
-36               -36

b^2 = 64

b = 8

b is the same thing as your "x", so x = 8