#include <fstream.h>
#include <stdio.h>
#include <math.h>
#include <string.h>

const double D = 6875.;
const double R = 3437.5;
const double C_PI = 3.14159265358979323846;

int main ()
{
  double phi1, phi2, teta1, teta2;
  double degrees, minutes, seconds, sign;
  double x1,x2,y1,y2,z1,z2;
  char s[300];

  cin.getline(s, 299);
  cin.getline(s, 299);
  cin.getline(s, 299);
  // read the ship coordinates
  cin.getline(s, 299);

  degrees = atof(s);

  char *p = strchr(s,'^');
  minutes = atof(p + 1);

  p = strchr(s, '\'');
  seconds = atof(p + 1);

  sign = 0.;
  if (strstr(s, "SL") != NULL) sign = -1.;
  if (strstr(s, "NL") != NULL) sign = 1.;

  phi1 = sign * (degrees + minutes / 60. + seconds / 3600.);

  cin >> s;
  cin.getline(s, 299);

  degrees = atof(s);

  p = strchr(s, '^');
  minutes = atof(p + 1);

  p = strchr(s, '\'');
  seconds = atof(p + 1);

  sign = 0.;
  if (strstr(s,"WL") != NULL) sign=-1.;
  if (strstr(s,"EL") != NULL) sign=1.;

  teta1 = sign * (degrees + minutes / 60. + seconds /
3600.);

  // skip one line
  cin.getline(s, 299);
  // read the iceberg coordinates

  cin.getline(s, 299);
  p = strchr(s,'^');
  degrees = atof(s);
  minutes = atof(p+1);

  p = strchr(s, '\'');
  seconds = atof(p+1);

  sign = 0.;
  if (strstr(s, "SL") != NULL) sign=-1.;
  if (strstr(s, "NL") != NULL) sign=1.;

  phi2 = sign * (degrees + minutes / 60. + seconds / 3600.);

  cin >> s;
  cin.getline(s, 299);
  degrees = atof(s);
  p = strchr(s,'^');
  minutes = atof(p + 1);

  p = strchr(s, '\'');

  seconds = atof(p + 1);

  sign = 0.;
  if (strstr(s, "WL") != NULL) sign = -1.;
  if (strstr(s, "EL") != NULL) sign = 1.;
  teta2 = sign * (degrees + minutes / 60. + seconds /
3600.);

  // calculate the euclids coordinate
  phi1  = phi1  * C_PI / 180.;
  phi2  = phi2  * C_PI / 180.;
  teta1 = teta1 * C_PI / 180.;
  teta2 = teta2 * C_PI / 180.;

  x1 = R * cos(phi1) * cos(teta1);
  y1 = R * cos(phi1) * sin(teta1);
  z1 = R * sin(phi1);

  x2 = R * cos(phi2) * cos(teta2);
  y2 = R * cos(phi2) * sin(teta2);
  z2 = R * sin(phi2);

  double dist = sqrt((x1-x2) * (x1-x2) + (y1-y2) * (y1-y2)
+ (z1-z2) * (z1-z2));
  double k = dist / D;
  double way = D * asin(k);

  printf("The distance to the iceberg: %4.2lf miles.\n",
way);
  if ( way < 100.00 ) printf("DANGER\n");

  return 0;
}

Try

if (way < 99.95) ...

Maybe you should try specifying your headers.
> #include <fstream.h>
> #include <stdio.h>
> #include <math.h>
> #include <string.h>
>
> const double D = 6875.;
> const double R = 3437.5;
> const double C_PI = 3.14159265358979323846;
>
> int main ()
> {
>   double phi1, phi2, teta1, teta2;
>   double degrees, minutes, seconds, sign;
>   double x1,x2,y1,y2,z1,z2;
>   char s[300];
>
>   cin.getline(s, 299);
>   cin.getline(s, 299);
>   cin.getline(s, 299);
>   // read the ship coordinates
>   cin.getline(s, 299);
>
>   degrees = atof(s);
>
>   char *p = strchr(s,'^');
>   minutes = atof(p + 1);
>
>   p = strchr(s, '\'');
>   seconds = atof(p + 1);
>
>   sign = 0.;
>   if (strstr(s, "SL") != NULL) sign = -1.;
>   if (strstr(s, "NL") != NULL) sign = 1.;
>
>   phi1 = sign * (degrees + minutes / 60. + seconds / 3600.);
>
>   cin >> s;
>   cin.getline(s, 299);
>
>   degrees = atof(s);
>
>   p = strchr(s, '^');
>   minutes = atof(p + 1);
>
>   p = strchr(s, '\'');
>   seconds = atof(p + 1);
>
>   sign = 0.;
>   if (strstr(s,"WL") != NULL) sign=-1.;
>   if (strstr(s,"EL") != NULL) sign=1.;
>
>   teta1 = sign * (degrees + minutes / 60. + seconds /
> 3600.);
>
>   // skip one line
>   cin.getline(s, 299);
>   // read the iceberg coordinates
>
>   cin.getline(s, 299);
>   p = strchr(s,'^');
>   degrees = atof(s);
>   minutes = atof(p+1);
>
>   p = strchr(s, '\'');
>   seconds = atof(p+1);
>
>   sign = 0.;
>   if (strstr(s, "SL") != NULL) sign=-1.;
>   if (strstr(s, "NL") != NULL) sign=1.;
>
>   phi2 = sign * (degrees + minutes / 60. + seconds / 3600.);
>
>   cin >> s;
>   cin.getline(s, 299);
>   degrees = atof(s);
>   p = strchr(s,'^');
>   minutes = atof(p + 1);
>
>   p = strchr(s, '\'');
>
>   seconds = atof(p + 1);
>
>   sign = 0.;
>   if (strstr(s, "WL") != NULL) sign = -1.;
>   if (strstr(s, "EL") != NULL) sign = 1.;
>   teta2 = sign * (degrees + minutes / 60. + seconds /
> 3600.);
>
>   // calculate the euclids coordinate
>   phi1  = phi1  * C_PI / 180.;
>   phi2  = phi2  * C_PI / 180.;
>   teta1 = teta1 * C_PI / 180.;
>   teta2 = teta2 * C_PI / 180.;
>
>   x1 = R * cos(phi1) * cos(teta1);
>   y1 = R * cos(phi1) * sin(teta1);
>   z1 = R * sin(phi1);
>
>   x2 = R * cos(phi2) * cos(teta2);
>   y2 = R * cos(phi2) * sin(teta2);
>   z2 = R * sin(phi2);
>
>   double dist = sqrt((x1-x2) * (x1-x2) + (y1-y2) * (y1-y2)
> + (z1-z2) * (z1-z2));
>   double k = dist / D;
>   double way = D * asin(k);
>
>   printf("The distance to the iceberg: %4.2lf miles.\n",
> way);
>   if ( way < 100.00 ) printf("DANGER\n");
>
>   return 0;
> }
>

change 'way<100.00' to '100.00-way>0.005'
then you will got accept;
Good luck!

Thanks a lot!
Got AC!