Originally Posted by

**Zion** Since it's a right triangle you need to use the pythagorean theorem...

$\displaystyle x^2 + y^2 = z^2$

And since we are dealing with rates you need to derive the equation

$\displaystyle 2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 2z\frac{dz}{dt}$

The 2's cancel so we're left with

$\displaystyle x\frac{dx}{dt} + y\frac{dy}{dt} = z\frac{dz}{dt}$

now what we're looking for is how fast the hypotenuse is changing, $\displaystyle \frac{dz}{dt}$

and what we are given is

$\displaystyle x = 6$

$\displaystyle \frac{dx}{dt} = 0$

$\displaystyle y=8$ Use pythagorean theorem here to get $\displaystyle y$

$\displaystyle \frac{dy}{dt} = 2 $

and

$\displaystyle z = 10$

then we just solve

$\displaystyle x\frac{dx}{dt} + y\frac{dy}{dt} = z\frac{dz}{dt}$

$\displaystyle 0 + 8*2 = 10\frac{dz}{dt}$

$\displaystyle \frac{dz}{dt} = \frac{16}{10} = 1.6$

Hope this helps! it's my first time posting a reply so sorry if it's unclear, let me know if you have any questions