Angle of Incidence of a Tail-dragger

I was designing a tail-dragger and through online sources I realised that the angle of the plane when grounded is supposed to be within a range of 10⁰ to 20⁰. Now there are many variables that can be altered so as to change the AoA of the plane (when grounded), which means that the number of iterations are too large for manual calculation. MATLAB came to my rescue.
2. Logic
• 1st of all I wrote down all the variables involved and assigned a particular value or a range of values for each variable.
• Then I formed 3 different equations that related these variables with one another. These equations are written in terms of the ‘α’ (the AoA of the plane).
• If you were to observe the diagram you will notice that each of these three α is independent of one other in terms of the 3 equations formed. For instance, if α₁ = 15⁰ for a certain set of values of variables, then it isn’t necessary for α₂ and α₃ to obtain a value of 15⁰ for the same set of values of variables.
• Thus to obtain the correct set of values for each variable, I find the intersection of α₁, α₂ and α₃ by equating them and assign a common name ‘α’. In other words we are solving the 3 equations simultaneously to obtain a common α.
Note: I have rounded off the values of α₁, α₂ and α₃, otherwise it would be impossible to find an intersection of their values. Also I have created a function ‘RD’ that converts ‘radian’ into ‘degree’, you can create that with ease.
• Using the above logic, I have written a MATLAB code that will give me an output only if the value of α is within a desired range of values. This code helps us figure out various sets of values that the other variables can assume so as to obtain the desired α.
• The best part is that it gives us many “sets of values” that the variables can assume, meaning we can select the set that is most suitable for the ease of construction of our plane!