[SOLVED] How to find the angles of the faces of a scalene tetrahedron given lengths of edges

I'm writing a program in C to determine the apex of a tetrahedron given the given the lengths of all its edges. The tetrahedron has an equilateral base and scalene sides. In order to complete the formula, I need a way of getting the angle between a face and the equilateral base. I know the height of the altitude of one of the faces, and once I can get the angle between a face and the base, I can rotate the height by that angle and get the position of the apex.

I have 0 idea where to begin figuring out the formula for the angle(see theta below), and how to translate it into C.

I know the lengths of the segments in yellow and am trying to find angle B in blue

Here's my code so far:

#include <math.h>
#include <stdio.h>
#include <time.h>
#include <stdlib.h>

typedef struct {
  float x;
  float y;
  float z;
} Point;

typedef struct {
  float edgeA, edgeB, edgeC;
  float legA, legB, legC;
  Point vertexBaseA, vertexBaseB, vertexBaseC;
  Point apex;
} scaleneTetrahedron;

Point p(float x,float y) {
    Point pt; pt.x = x; pt.y = y; pt.z =0;return pt;
}

Point pZ(float x, float y, float z) {
      Point pt; pt.x = x; pt.y = y;pt.z =z; return pt;
}

void printPoint(char *identifier, Point p){
  printf("(%s: %f, %f, %f)\n",identifier, p.x,p.y,p.z);
}

void printFloat(float n) {
  printf("%f",n);
}

scaleneTetrahedron sT_Hedron(float lengthsEdges[3],float lengthsLegs[3],Point vertexBases[3]) {
  scaleneTetrahedron h;
  h.edgeA = lengthsEdges[0], h.edgeB = lengthsEdges[2], h.edgeC = lengthsEdges[2];
  h.legA = lengthsLegs[0], h.legB = lengthsLegs[1],h.legC = lengthsLegs[2];
  h.vertexBaseA = vertexBases[0], h.vertexBaseB = vertexBases[1], h.vertexBaseC = vertexBases[2];
  return h;
}

#define rt(n) (sqrt(n))
float SQUARE(float n) {return n*n;}
float PERP(float slope) { return 1/slope * -1;}
float Rad_To_Deg(float angle) {return angle*57.29577951f;}

#define ANGLE_FOR(rangX,rangY)      ( Rad_To_Deg(atan2(rangX,rangY))     )

float DISTANCE(Point v1, Point v2){
  return sqrtf(SQUARE(v1.x-v2.x) + SQUARE(v1.y-v2.y));

}

float WIDTH(float leg1,float leg2,float base){
  float ret = ((SQUARE(leg1) - SQUARE(leg2)) + SQUARE(base)) / (2 * base);
  printf("Ret is:%f\n",ret);
  return ret;
}

float HEIGHT(float width,float leg1){
  float ret = sqrtf(SQUARE(leg1) - SQUARE(width));
  return ret;
}

float slopeFor(Point A, Point B) {
  return (B.y-A.y) / (B.x - A.x);
}

float yInterceptFor(float slope, Point A) {
  return (A.y - (slope * A.x));
}

float map(float range1_A, float range1_B, float range2_A, float range2_B, float value) {
    float  inMin = range1_A;
    float  inMax = range1_B;

    float  outMin = range2_A;
    float  outMax = range2_B;

    float input = value;
    float output = outMin + (outMax - outMin) * (input - inMin) / (inMax - inMin);

    return output;
}

Point XYAltitude(float leg1, float leg2, float base) {

  float width = WIDTH(leg1,leg2,base); 
  float height = HEIGHT(width,leg1);
  return p(width, height);
}

Point APEX_OF(scaleneTetrahedron shape) {
  Point altitude1 = XYAltitude(shape.legA,shape.legB, shape.edgeA);//Getting the x position of the altitude of faceA and the height of the altitude. 
  printPoint("Altitude face:",altitude1);
  float 
  x = altitude1.x,
  baseX1 = x,
  baseX2 = x,
  baseY1 = 0,
  baseY2 = 10
  ; 

  float slopeBase = slopeFor(shape.vertexBaseC, shape.vertexBaseB), yIntBase = yInterceptFor(slopeBase,shape.vertexBaseB);
  printf("slope is:%f ,yint is:%f, point of intersection:%f\n",slopeBase,yIntBase, (slopeBase * x)+yIntBase);
  Point intersectionBase = p(x, (slopeBase * x) + yIntBase);


  printPoint("IntersectionBase:",intersectionBase);

  float zIntersectionBase = (slopeBase * x) + yIntBase;//it is "y" because we are switching from a topdown to a side view
  float zHypotenuse = (shape.edgeC* intersectionBase.y)/shape.vertexBaseC.y; //THIS IS THROWING OFF THE MEASUREMENT: sqrtf(SQUARE(zIntersectionBase) + SQUARE(altitude1.y));
  Point zAltitude   = XYAltitude(altitude1.y,zHypotenuse,zIntersectionBase);
  float theta       = Rad_To_Deg(atan2(zAltitude.x,zAltitude.y));//Here's where I am having trouble.
  float y = Rad_To_Deg(sin(theta)) * altitude1.x;
  float z = Rad_To_Deg(cos(theta)) * altitude1.x;
  printFloat(theta);
  Point rtd;
  rtd.x = x;
  rtd.z = y; //Only now did I learn that z and y are swapped in 3D. But, this is no problem due to abstraction. 
  rtd.y = z;

  return rtd;
}

int main(int argc, const char *argv[]){
  // srand(time(NULL));   

  Point vertexA  = p(0,0); 
  Point vertexB  = p(3,0.f);
  Point vertexC  = p(1.5,2.6); 
  Point apex =   pZ(1.5,0.87,2.45);

  float baseA = DISTANCE(vertexA,vertexB);
  float baseB = DISTANCE(vertexB,vertexC);
  float baseC = DISTANCE(vertexC,vertexA);
  float legA  = DISTANCE(vertexA,apex);
  float legB  = DISTANCE(vertexB,apex);
  float legC  = DISTANCE(vertexC,apex);

  scaleneTetrahedron toSend;
  toSend.edgeA = baseA;
  toSend.edgeB = baseB;
  toSend.edgeC = baseC;

  toSend.legA = legA; 
  toSend.legB = legB;
  toSend.legC = legC;

  toSend.vertexBaseA = vertexA;
  toSend.vertexBaseB = vertexB;
  toSend.vertexBaseC = vertexC;
  printPoint("APEX:",APEX_OF(toSend));

  return 0;

}