Let the coordinates of A be (0, 0) and B (0, 633). C is 257 someunits (let's say meters, we don't care) from A and 390 m from B.

Distance A-C:  sqrt (x² + y²) = 257          <=> x² + y² = 257²           (1)
Distance B-C:  sqrt (x² + (633 - y)²) = 390  <=> x² + (633 - y)² = 390²   (2)
Substrating 2 from 1:  y² - (633 - y)² = 257² - 390²
<=> (y + a - y)(y - a + y) = 257² - 390²
<=> a (2 y - a) = 257² - 390²
<=> y = (257² - 390²) / 2a + a/2

Similarly:
x² + y² = 257²
<=> x = +/- sqrt ( 257² - y²)

##</code><code>##

use strict;  
use warnings;

my %coordinates;
$coordinates{A} = [0,0];
$coordinates{B} = [0,633];
$coordinates{C} = find_coord(257, 390, undef);
$coordinates{D} = find_coord(91, 661, 228);

print "@{$coordinates{D}} \n";


sub find_coord {
	my ($a, $b, $c) = @_;
	my $sq_dist_dif = $a*$a - $b*$b;
	my $y = $sq_dist_dif/(633*2) + 633/2;
	my $x = sqrt ($a*$a - $y*$y);
	return [$x, $y] unless defined $c;
	my $dist_2_c_1 = distance ([$x, $y], $coordinates{C}, $c);
	my $dist_2_c_2 = distance ([-$x, $y], $coordinates{C}, $c);
	$dist_2_c_1 < $dist_2_c_2 ? [$x, $y, $dist_2_c_1] : [-$x, $y, $dist_2_c_2];
}
sub distance {
	return abs (sqrt (($_[0][0] - $_[1][0])**2 + ($_[0][1] - $_[1][1])**2) - $_[2]);
}

##</code><code>##

use strict;  
use warnings;
use Data::Dumper;

my %coordinates;
$coordinates{A} = [0,0];
$coordinates{B} = [0,90];

while (<DATA>) {
	my ($site, $dA, $dB, $dC) = /(\w):\s+(\d+)\s+(\d+)\s+(\d+)/;
	$coordinates{$site} = find_coord ($dA, $dB, $dC);
}
print Dumper \%coordinates;

sub find_coord {
	my ($a, $b, $c) = @_;
	my $sq_dist_dif = $a*$a - $b*$b;
	my $y = $sq_dist_dif/(90*2) + 90/2;
	my $x = sqrt ($a*$a - $y*$y);
	return [$x, $y] unless $c;
	my $dist_2_c_1 = distance ([$x, $y], $coordinates{C}, $c);
	my $dist_2_c_2 = distance ([-$x, $y], $coordinates{C}, $c);
	$dist_2_c_1 < $dist_2_c_2 ? [$x, $y, $dist_2_c_1] : [-$x, $y, $dist_2_c_2];
}
sub distance {
	return abs (sqrt (($_[0][0] - $_[1][0])**2 + ($_[0][1] - $_[1][1])**2) - $_[2]);
}

__DATA__
C: 64  76  0
D: 28  70  74
E: 120  62  68
F: 68  52  93
G: 53  125 64

##</code><code>##

$ perl  coordinates2.pl
$VAR1 = {
          'F' => [
                   '-39.0540935398867',
                   '55.6666666666667',
                   '1.33876031467558'
                 ],
          'A' => [
                   0,
                   0
                 ],
          'D' => [
                   '-17.1497975368678',
                   '22.1333333333333',
                   '2.41895858461325'
                 ],
          'C' => [
                   '53.1402755816047',
                   '35.6666666666667'
                 ],
          'G' => [
                   '46.0712491690859',
                   '-26.2',
                   '1.73078144969754'
                 ],
          'E' => [
                   '60.4799895486306',
                   '103.644444444444',
                   '0.372872345124534'
                 ],
          'B' => [
                   0,
                   90
                 ]
        };

##</code><code>##

A 0 0
B O 90
C 55 35
D -20 20
E 60 114
F 64 55
G 45 -29