Answer
$75\sqrt2$ miles, 106.1 miles
Work Step by Step
$x=$ distance of one ship
$x^2+x^2=150^2$
$2x^2=22500$
$2x^2/2=22500/2$
$x^2=11250$
$\sqrt {x^2} = \sqrt{11250}$
$x = ± \sqrt {2*5625}$
$x = ± \sqrt {2*75*75}$
$x = ± 75 \sqrt 2$
We are looking for a distance, so we use the positive square root of 2.
$x= 75 \sqrt 2$
$\sqrt 2 = 1.414$
$75*1.414 = 106.066$
$106.066$
$106.1$
