Can anyone explain why I was incorrect in this problem: 
I used a tetrahedron solver online, http://rechneronline.de/pi/tetrahedron.php, and it says I have the right answer.
Can anyone explain why I was incorrect in this problem: 
I used a tetrahedron solver online, http://rechneronline.de/pi/tetrahedron.php, and it says I have the right answer.
Assuming that $S$ denotes the length of a side, your answer is correct. See here.