Answer
$ x=y= 4.42\ m$
Work Step by Step
We know the cable is 8 meters long so:
$r = 8\ m$
We also know that:
$z = 5\ m$
$x= y$
Calculating:
$r = [xi + yj + 5k]\ m$
$r = \sqrt{(x)^2 + (y)^2 + (z)^2}$
Substitute the known values:
$8 = \sqrt{(x)^2 + (y)^2 + (5)^2}$
As x=y:
$8 = \sqrt{(x)^2 + (x)^2 + (5)^2}$
Rearrange the equation to calculate:
$8^2 = 2x^2 + (5)^2 \Rightarrow 64 = 2x^2 + 25$
$64 - 25 = 2x^2 \Rightarrow x^2 = \dfrac{39}{2}$
$x = \sqrt{\dfrac{39}{2}} = 4.42\ m$
Then:
$x= y = 4.42\ m$
