traingle_x_problem.cpp

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

#define PI 3.14159265

/*
 *  a1  \           a1  \
 *      |\              |\ s3            ______ a22
 *      | \ s3      s21 | \              |    /
 *      |  \            |  \         s22 |  / s1
*  s2  |   \           |___\ a21     a3 |/ 
*      |    \ a2                       
*      |   /
*      | / s1
*  a3  /
*/


void solve_triangle(double a1, double a2, double a3,
                    double&s1, double&s2, double&s3) {
    
    double a21 = 90 - a1;
    
    s3         = 1.0 / ( cos(a21*PI/180.0) );
    double s21 = tan(a21*PI/180.0);
    
    double a22 = a2-a21;
    s1         = 1.0 / ( cos(a22*PI/180.0) );
    double s22 = tan(a22*PI/180.0);
    s2         = s21 + s22;
    
}

void divide(double&v1, double&v2, double&v3, double q) {
    v1 = v1 / q;
    v2 = v2 / q;
    v3 = v3 / q;
}


int main () {
    
    double CEDc, CEDe, CEDd, AECa, AECe, AECc, BEDb, BEDe, BEDd;
    double ACDa, ACDc, ACDd, BDCb, BDCd, BDCc;
    double AEBa, AEBe, AEBb;
    
    solve_triangle(60,    70, 50, CEDc, CEDe, CEDd);
    solve_triangle(50,   110, 20, AECa, AECe, AECc);
    solve_triangle(40,   110, 30, BEDb, BEDe, BEDd);
    solve_triangle(50, 20+60, 50, ACDa, ACDc, ACDd);
    solve_triangle(40, 30+50, 60, BDCb, BDCd, BDCc);
    
    divide(CEDc, CEDe, CEDd, CEDe/1.0   );  // CEDe := 1
    divide(AECa, AECe, AECc, AECa/CEDd  );  // AECa := CEDd
    divide(BEDb, BEDe, BEDd, BEDb/CEDc  );  // BEDb := CEDc
    divide(ACDa, ACDc, ACDd, ACDa/1.0   );  // ACDa := 1
    divide(BDCb, BDCd, BDCc, BDCb/1.0   );  // BDCb := 1
    
    AEBa = BDCd - CEDd;
    AEBb = ACDc - CEDc;
    
    // Law of cosines
    AEBe = sqrt( pow(AEBa, 2) + pow(AEBb, 2) - 2 * AEBa * AEBb * cos(70*PI/180.0));
    
    // Law of sines
    double BAE = asin( sin(70*PI/180.0) * AEBa / AEBe )*180.0/PI;
    
    printf("BAE:%f", BAE);
    // 80.00
    
}