PowerShell: 111
Golfed Code
1..2|%{sv $_ (read-host)};"The hypotenuse of this right triangle is $("{0:N3}"-f[math]::sqrt($1/1*$1+$2/1*$2))"
Walkthrough
1..2|%{sv $_ (read-host)};
Gets two inputs interactively from the user, and stores them in $1 and $2. Might be able to cut some length by using arguments or pipeline inputs instead.
"The hypotenuse of this right triangle is
Required text in the output, per the challenge specifications.
$(
...)"
Encapsulated code block will be processed as script before being included in the output.
"{0:N3}"-f
Formats output from the next bit of code as a number with exactly three digits after the decimal point.
[math]::sqrt(
...)
Gets the square root of the encapsulated value.
$1/1*$1+$2/1*$2
Serves as our "a^2+b^2". Multiplying a number by itself is the shortest way to square it in PowerShell, but the variables need to be divided by 1 first to force them to integers. Otherwise, they are treated as text and 3*3+4*4 would be 3334444 instead of 25.