$ perl slope5.pl
Can't use string ("4.3125") as an ARRAY ref while "strict refs" in use
+ at ../utils1.pm line 39.
$ cat slope5.pl
#!/usr/bin/perl -w
use strict;
use 5.010;
use Math::Trig;
BEGIN { push @INC, ".."; }
use utils1;

my @AoA;
my $aoa_ref = \@AoA;
my @vector = (4.3125, 0.4375);
push @AoA, @vector;
@vector = (4.375, 0.375);
push @AoA, @vector;
@vector = (4.4375, 0.375);
print_aoa($aoa_ref);
__END__ 
$
[download]

Thought I would be comparing hypotenuses to heights but can't see why perl doesn't this is ok.

The error occurs in the module, but the coding error is actually located in your calling program. When you do this:

my @vector = (4.3125, 0.4375);
push @AoA, @vector;
@vector = (4.375, 0.375);
push @AoA, @vector;
[download]

you are not creating an array of arrays (AoA), but a simple array whose 4 elements are:

(4.3125, 0.4375, 4.375, 0.375)
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You need to push on @AoA a reference to @vector:

my @vector = (4.3125, 0.4375);
push @AoA, \@vector;
@vector = (4.375, 0.375);
push @AoA, \@vector;
[download]

or build directly an array reference:

push @AoA, [4.3125, 0.4375];
push @AoA, [4.375, 0.375];
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I guess this should solve your issue.

As I said earlier, you should avoid using the $a and $b variables, they are special variables used among other things for sorting, they behave differently from other variables, and using as you do them might lead to difficult-to-track bugs. You may use $c or $d, if you like, this will not be a problem, but I would personally put a more meaningful name helping comprehension of what they represent.

Update: As pointed below by farang the first method above for building an AoA is actually buggy. Use the second one. Thanks to farang for picking that.

You need to push on @AoA a reference to @vector:

my @vector = (4.3125, 0.4375);
push @AoA, \@vector;
@vector = (4.375, 0.375);
push @AoA, \@vector;
[download]

That way is buggy, though, as the redefinition of @vector will clobber the first pushed array element. This is explained under COMMON MISTAKES in perldsc, "taking a reference to the same memory location repeatedly".

So both lines above should instead use a square bracket reference.

push @AoA, [ @vector ];
[download]

$ perl sill2.pl
elt 0 0 is 0.4375
elt 0 1 is 4.3125
elt 0 2 is bath-left
elt 1 0 is 0.375
elt 1 1 is 4.375
elt 1 2 is bath-middle
elt 2 0 is 0.375
elt 2 1 is 4.4375
elt 2 2 is bath-right
bath-left has slope 5.82263230478133
bath-middle has slope 4.91710033552881
bath-right has slope 4.84767847916148
$ cat sill2.pl
#!/usr/bin/perl -w
use strict;
use 5.010;
use Math::Trig;
BEGIN { push @INC, ".."; }
use utils1;

my @AoA;
my $aoa_ref = \@AoA;
my $vector_ref = [0.4375, 4.3125, "bath-left"];
push @AoA, $vector_ref;
$vector_ref = [0.375, 4.375,  "bath-middle"];
push @AoA, $vector_ref;
$vector_ref = [0.375,4.4375, "bath-right"];
push @AoA, $vector_ref;
print_aoa($aoa_ref);
for my $i ( 0 .. $#AoA ) {
   my $ratio = $AoA[$i][0]/$AoA[$i][1];
   my $rad = asin($ratio);
   my $degrees  = rad2deg($rad);
   my $name = $AoA[$i][2];
   say "$name has slope $degrees";
   }
__END__ 
$
[download]

This might be the most robust version of this material.

Your error is in the ../utils1.pm module, but you don't show the code for that module. Difficult to help you in such conditions.

$ cd ..
$ pwd 
/home/fred/Desktop/root3/pages/sills/template_stuff
$ ls
aimages          config1.pm               lime1.css     pm4.txt
basketball1.css  football1.pm             mango1.css    rebus1.tmpl
bathfan1.css     football2.pm             marvin1.css   rebus2.tmpl
blue1.css        footer_center2.txt       math1.pm      rebus3.tmpl
bom              footer_center_begin.txt  nibley1.pm    rebus4.tmpl
bottom1.txt      footer_center.txt        oibottom.txt  rory1.css
captions         giles1.css               oitop.txt     ruscaptions
ceres1.css       hc_input2.txt            pears1.css    sills1.css
code1.tmpl       hc_input.txt             plum1.css     utils1.pm
code2.tmpl       html1.pm                 pluto1.css    utils1.pm~
code3.tmpl       lemon1.css               pm1.txt       watermelon1.cs
+s
$ cat utils1.pm
package utils1;
require Exporter;
use config1;

our @ISA = qw(Exporter);
our @EXPORT = qw( invert_aoa print_hash print_aoa
highest_number get_list zip_lists p_tag);

sub invert_aoa{
use strict;
use warnings;
use 5.010;

my $a = shift;
my @AoA = @$a;
my $k = $#AoA;
#say "k is $k"; 
my @BoB;
    for my $i ( 0 .. $#AoA ) {
        my $aref = $AoA[$i];
        my $x = $#{$aref};
        #say "x is $x";
        for my $j ( 0 .. $#{$aref} ) {
            $BoB[$j][$i]= $AoA[$i][$j];
        }
    }
my $b = \@BoB;
return $b;
}
sub print_aoa{
use strict;
use warnings;
use 5.010;

my $a = shift;
my @AoA = @$a;
    for my $i ( 0 .. $#AoA ) {
        my $aref = $AoA[$i];
        for my $j ( 0 .. $#{$aref} ) {
            print "elt $i $j is $AoA[$i][$j]\n";
        }
    }
return $a;
}

sub highest_number{
use strict;
use File::Basename;
use Cwd;

my ($aref, $filetype, $word) = @_;
my $number;
my @matching;
my $ext = ".".$filetype;
push (@matching, 0); #min returned value
for my $file (@{$aref}) {
#print "file is $file\n";
if ($file =~ /^$word(\d*)$ext$/){
   #print "matching is $file\n";
   push (@matching, $1);
   }
}
@matching = sort @matching;
my $winner  = pop @matching;
return $winner  
}

sub print_hash{
   my $hash_ref = shift;
   print "subroutine says this is your hash: \n";
   my %hash = %$hash_ref;
   while ( (my $key,my $value) = each %hash )
   {
      print "key: $key, value: $hash{$key}\n";
   }
}

sub get_list{
use strict;
use warnings;
use 5.010;
use File::Slurp;

my $file = shift;
my @lines = read_file($file);
chomp(@lines); 
s/^\s+|\s+$//g for @lines;
@lines = grep length, @lines;
return @lines;
}

sub zip_lists  {
use strict;
use warnings;
use 5.010;
use List::MoreUtils qw( zip );

my ($file1, $file2) = @_;
my @file1lines = get_list($file1);
my @file2lines = get_list($file2);
say "keys are @file1lines";
say "values are @file2lines";
my %hash = zip @file1lines, @file2lines;
return \%hash;
}

sub p_tag  {
use strict;
use warnings;

my $text = shift;
my $before = '<p>';
my $after = '</p>';
my $return = $before.$text.$after;
return \$return;
}

1;

$
[download]

What I found when field measuring was that it was much more attainable to get hypotenuses and heights, so that left me looking for arcsin. I had hoped to get this processed as an AoA, but I'm not quite there yet....

$ perl slope8.pl
bath-left
theta is 5.82263230478133
bath-middle
theta is 4.91710033552881
bath-right
theta is 4.84767847916148
dining-south
theta is 15.2575232904564
john-north
theta is 16.0133944239485
middle-front
theta is 24.6243183521641
south-front
theta is 14.4775121859299
$ cat slope8.pl
#!/usr/bin/perl -w
use strict;
use 5.010;
use Math::Trig;
BEGIN { push @INC, ".."; }
use utils1;

my @AoA;
my $aoa_ref = \@AoA;

my $tja = 0.4375/4.3125;
say "bath-left";
my $hja = asin $tja;
my $degrees  = rad2deg($hja);
say "theta is $degrees";

$tja = 0.375/4.375;
$hja = asin $tja;
say "bath-middle";
$degrees  = rad2deg($hja);
say "theta is $degrees";

say "bath-right";
$tja = 0.375/4.4375;
$hja = asin $tja;
$degrees  = rad2deg($hja);
say "theta is $degrees";

say "dining-south";
$tja = 1.25/4.75;
$hja = asin $tja;
$degrees  = rad2deg($hja);
say "theta is $degrees";

say "john-north";
$tja = 1.0/3.625;
$hja = asin $tja;
$degrees  = rad2deg($hja);
say "theta is $degrees";

say "middle-front";
$tja = 1.875/4.5;
$hja = asin $tja;
$degrees  = rad2deg($hja);
say "theta is $degrees";

say "south-front";
$tja = 1.125/4.5;
$hja = asin $tja;
$degrees  = rad2deg($hja);
say "theta is $degrees";
__END__ 
$
[download]