Don't use function parameters as local variables!
And you never call berechnung_beta.
Code:
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
 
#define TOTAL_DEG 180.0
 
double berechnung_length(double a, double b, double gamma)
{   
    return sqrt(a * a + b * b - (2 * a * b * cos(gamma)));
}
  
double berechnung_alpha(double a, double b, double c, double gamma)
{
    return gamma * acos((double)(b * b + c * c - a * a) / (2.0 * b * c));;
}
 
double berechnung_beta(double gamma, double alpha)
{
    return -gamma - alpha + TOTAL_DEG;
}
 
int main()
{
    double a, b, gamma;
    printf("Bitte gib a, b und gamma eines Dreiecks ein\n");
    scanf("%lf %lf %lf",&a,&b,&gamma);
 
    double laenge = berechnung_length(a,b,gamma);
    double alpha = berechnung_alpha(a,b,laenge,gamma);
    double beta = berechnung_beta(gamma, alpha);
 
    printf("a = %lf\t b = %lf\t gamma = %lf\n",a,b,gamma);
    printf("Daraus folgt c = %lf, alpha = %lf und beta = %lf\n",
        laenge, alpha, beta);
}
If it still gives wrong answers, you need to tell us what inputs you are using and what output you expected.