Answer
16 ft
Work Step by Step
$x^2+(x+10)^2=40^2$
$x^2+x*x+10*x+x*10+10*10=1600$
$x^2+x^2+20x+100=1600$
$2x^2+20x-1500=0$
$2(x^2+10x-750)=0$
$2(x^2+10x-750)/2=0/2$
$x^2+10x-750=0$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-10±\sqrt {10^2-4*1*-750})/2*1$
$x=(-10±\sqrt {100+3000})/2$
$x=(-10±\sqrt {3100})/2$
$x=(-10±\sqrt {775*4})/2$
$x=(-10±2\sqrt {775})/2$
$x=-5±\sqrt {775}$
$x=-5±27.84$
We are talking about a distance, so we don't want the negative square root.
$x=-5+27.84$
$x=22.84$
$22.84+22.84+10-40$
$45.68-30$
$15.68$
