L1  =  
      10;  L2  =  5;

X  = 
        3.5;
Y  =  4;

t  =  
        2*L1*Sqrt[X*X + Y*Y];
thetaT  =  ArcCos[X/Sqrt[X*X + Y*Y]]; 
    theta1  =  
      ArcCos[(L1*L1 + X*X + Y*Y - L2*L2)/t] + 
        thetaT;
theta2  =  
        ArcCos[-(L1*L1 + L2*L2 - (X*X + Y*Y))/(2*L1*
                L2)];

x1  = 
        L1* Cos[theta1];
y1  =  L1*Sin[theta1];

x2  =  
        x1 + L2*Cos[theta1 - theta2];
y2  =  y1 + L2*Sin[theta1 - theta2];

p = 
        Point[{X, Y}];
  g  =  
        Line[{{0, 0}, {x1, y1}, {x2, y2}}];

Show[
        Graphics[{g, PointSize[0.02], p}], 
        Axes -> Automatic];

Sqrt[
      x1*x1 + y1*y1]

tx  =  
      x2 - x1; ty = y2 - y1;
Sqrt[tx*tx + ty*ty]