How to get bc to print trailing zeros?

In bc, the solution is to divide by 1:

$ bc -l <<<"scale=8; x=25*20; x"
500

$ bc -l <<<"scale=8; x=25*20; x/1"
500.00000000

So, your script could be like this:

hypothenuse () {
        local a b c x y
        a=${1}; b=${2}
        echo "This is a ${a} and b ${b}"
        x=$(echo "scale=8; $a^2/1" | bc -l)
        y=$(echo "scale=8; $b^2/1" | bc -l)
        echo "This is x ${x} and y ${y}"
#       local sum=`awk -v k=$x -v k=$y 'BEGIN {print (k + l)}'`
#       echo "This is sum ${sum}"
        c=$(echo "scale=8; sqrt($a^2 + $b^2)/1" | bc -l)
        echo "This is c ${c}"
}

I strongly suggest that you use $(…) instead of `…`.

But even that fails with values of 0.

The best solution is to let the scale of bc be 20 (from bc -l), make all the math required in one call to bc and then format the output as required with printf. Yes printf could format floats.

Assuming bash

hypothenuse () {  local a b c x y
                  a=${1:-0} b=${2:-0}
                  read -d '' x y c < <(
                  bc -l <<<"a=$a; b=$b; x=a^2; y=b^2; c=sqrt(x+y); x;y;c"
                  )

                  printf 'This is a %14.8f and b %14.8f\n' "$a" "$b"
                  printf 'This is x %14.8f and y %14.8f\n' "$x" "$y"
                  printf 'This is c %14.8f             \n' "$c"
               }

You can externalize formatting this way, using printf:

printf "%0.8f" ${x}

Example:

x=3
printf "%0.8f\n" ${x}
3.00000000

---

Note: printf output depends on your locale settings.

Just use awk:

$ cat tst.sh
#!/bin/env bash

hypothenuse() {
    awk -v a="$1" -v b="$2" 'BEGIN {
        printf "This is a %0.8f and b %0.8f\n", a, b
        c = sqrt(a^2 + b^2)
        printf "This is c %0.8f\n", c
    }'
}

hypothenuse "$@"

$ ./tst.sh 0 0
This is a 0.00000000 and b 0.00000000
This is c 0.00000000

$ ./tst.sh 17.12 23.567
This is a 17.12000000 and b 23.56700000
This is c 29.12898709