Solver SSS Triangle Solver 3 sides

Source code of ' SSS Triangle Solver 3 sides'

This Solver ( SSS Triangle Solver 3 sides) was created by by tomlaidlaw(14)

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About tomlaidlaw: 74 year old man interested in mathematical recreations.

==section input
<img src=http://tomlaidlaw.com/goatandsilo/circum.gif>
Input the following side lengths of the triangle:

a = *[input s1=2],b = *[input s2=3]and c = *[input s3=4]

Find the Angles, Area, incircle radius, circumcircle radius, and altitudes, (with formulas).

==section solution

perl

my $d1 = $s1 +$s2;
my $d2 = $s2 +$s3;
my $d3 = $s3 +$s1;

if($s1==0 || $s2==0 || $s3==0)
{
print " This is not a Triangle because atleast one of the side length is equal to zero. 
Please enter another set of values for a,b and c.";
}

elsif($d1==$s3 || $d2==$s1 || $d3==$s2)
{
print " This is not a Triangle because sum of two sides length is equal to the third side length.
Please enter another set of values for a,b and c.";
}

else 
{
  if(($s1+$s2<$s3) || ($s2+$s3<$s1) || ($s1+$s3<$s2) )
  {
print " These sides do not form a triangle. Please enter another set of values for a,b and c. 
";
  }

else
  {
  
print "Use Heron's Formula for Area:
First calculate s=(a+b+c)/2, then:
 <img src=http://tomlaidlaw.com/goatandsilo/herons-formula.gif>  
Use the Law of Cosines for the angles:
<img src=http://tomlaidlaw.com/goatandsilo/img36.gif>";

my $s = 1/2*($s1+$s2+$s3);
  my $K=sqrt($s*($s-$s1)*($s-$s2)*($s-$s3));
my $Kr=sprintf("%.3f", $K);

my $A1=(($s2*$s2+$s3*$s3-$s1*$s1)/(2*$s2*$s3));
my $A2=atan2(sqrt(1-$A1*$A1),$A1);
my $A2r=sprintf("%.3f",$A2);
my $A=$A2*180/3.14159;
my $Ar=sprintf("%.3f",$A);

my $B1=(($s1*$s1+$s3*$s3-$s2*$s2)/(2*$s1*$s3));
my $B2=atan2(sqrt(1-$B1*$B1),$B1);
my $B2r=sprintf("%.3f",$B2);
my $B=$B2*180/3.14159;  
my $Br=sprintf("%.3f",$B);

my $C1=(($s2*$s2+$s1*$s1-$s3*$s3)/(2*$s2*$s1));
my $C2=atan2(sqrt(1-$C1*$C1),$C1);
my $C2r=sprintf("%.3f",$C2);
my $C=$C2*180/3.14159;
my $Cr=sprintf("%.3f", $C);

my $R=.5*$s1/sin($A2);
my $Rr=sprintf("%.3f", $R);

my $r=2*$K/($s*2);
my $rr=sprintf("%.3f", $r);

my $ha=$s3*sin($B2);
my $har=sprintf("%.3f", $ha);

my $hb=$s1*sin($C2);
my $hbr=sprintf("%.3f", $hb);

my $hc=$s2*sin($A2);
my $hcr=sprintf("%.3f", $hc);
print
"
side a = $s1
side b = $s2
side c = $s3

AngleA = $Ar degrees or $A2r radians
AngleB = $Br degrees or $B2r radians
AngleC = $Cr degrees or $C2r radians

Area K = $Kr
 
Circumcircle Radius = $Rr __(R = .5a/sinA)
incircle radius = $rr __(r = 2K/(a+b+c))

height over side a = $har __(ha = csinB)
height over side b = $hbr __(hb = asinC)
height over side c = $hcr __(hc = bsinA)

Thanks to hummingbird for the use of his solver. Thanks to Wolfram Math World for the triangle graphic.
Tom Laidlaw
"
;

}
}
==section output
K,

==section check
  s1=4 s2=3 s3=5 a=3.464101615