Pythagorean Theorem Calculator

Question

My code seems a bit sloppy to me, but I don't know how to improve it to make it cleaner and more understandable. I'm just learning Python, as well as Tkinter. I figured a Pythagorean Theorem calculator should be a simple enough jumping-off point. The code works however, I don't have any tests in place so, at the moment you must use positive numbers as input in order to get a correct answer.

Things I would like to understand:

1. How to make better use of frames (at the moment I .pack_forget() the previous frame and create a new one)
2. I don't like the fact that I have functions within functions (need a better alternative)
3. I need to learn how to place labels and buttons better. (Lots of problems with grid() and pack())
4. When I make a frame solely for a label I would like to have a frame directly under that one where I can make a grid. (I suppose just use fill=X for the label and keep it all in one frame using grid())

from tkinter import *
from math import sqrt
root=Tk()
root.title("Pythagorean Theorem Calculator")
root.geometry("400x70")

f1=Frame(root, width=400, height=20)
f1.pack()
f2=Frame(root, width=420, height=20)
f2.pack()

var_a=StringVar()
var_b=StringVar()
var_c=StringVar()

# Initial welcome; then asks which side of triangle to solve for
def start():
    welcome_label=Label(f1, text="Welcome to the Pythagorean Theorem Calculator!", fg="red")
    solve_for=Label(f1, text="Would you like to solve for A, B, or C?")
    button_a=Button(f2, text="Solve for A", fg="red", command = solve_a)
    button_b=Button(f2, text="Solve for B", fg="red", command = solve_b)
    button_c=Button(f2, text="Solve for C", fg="red", command = solve_c)

    welcome_label.pack()
    solve_for.pack()
    button_a.pack(side=LEFT)
    button_b.pack(side=LEFT)
    button_c.pack(side=LEFT)


# Math, labels, buttons, and frames to solve for A
def solve_a():
    f1.pack_forget()
    f2.pack_forget()
    new_frame=Frame(root)
    new_frame.pack()

    def ans_a():
        new_frame.pack_forget()
        new_frame1=Frame(root)
        new_frame1.pack()
        value_b=float(var_b.get())
        value_c=float(var_c.get())
        a=sqrt((value_c**2)-(value_b**2))
        ans=Label(new_frame1, text=("The value of A is: "+str(a)))
        ans.pack()


    label_b=Label(new_frame, text="Value of B:")
    label_c=Label(new_frame, text="Value of C:")
    e1=Entry(new_frame, textvariable=var_b)
    e2=Entry(new_frame, textvariable=var_c)
    submit=Button(new_frame, text="Submit", fg="red", command=ans_a)

    label_b.grid(row=0, sticky=W)
    label_c.grid(row=1, sticky=W)
    e1.grid(row=0, column=1)
    e2.grid(row=1, column=1)
    submit.grid(row=2, column=1)



# Math, labels, buttons, and frames to solve for B
def solve_b():
    f1.pack_forget()
    f2.pack_forget()
    new_frame=Frame(root)
    new_frame.pack()

    def ans_b():
        new_frame.pack_forget()
        new_frame1=Frame(root)
        new_frame1.pack()
        value_a=float(var_a.get())
        value_c=float(var_c.get())
        b=sqrt((value_c**2)-(value_a**2))
        ans=Label(new_frame1, text=("The value of B is: "+str(b)))
        ans.pack()

    label_a=Label(new_frame, text="Value of A:")
    label_c=Label(new_frame, text="Value of C:")
    e1=Entry(new_frame, textvariable=var_a)
    e2=Entry(new_frame, textvariable=var_c)
    submit=Button(new_frame, text="Submit", fg="red", command=ans_b)

    label_a.grid(row=0, sticky=W)
    label_c.grid(row=1, sticky=W)
    e1.grid(row=0, column=1)
    e2.grid(row=1, column=1)
    submit.grid(row=2, column=1)



# Math, labels, buttons, and frames to solve for C
def solve_c():
    f1.pack_forget()
    f2.pack_forget()
    new_frame=Frame(root)
    new_frame.pack()

    def ans_c():
        new_frame.pack_forget()
        new_frame1=Frame(root)
        new_frame1.pack()
        value_a=float(var_a.get())
        value_b=float(var_b.get())
        c=sqrt((value_a**2)+(value_b**2))
        ans=Label(new_frame1, text=("The value of C is: "+str(c)))
        ans.pack()

    label_a=Label(new_frame, text="Value of A:")
    label_b=Label(new_frame, text="Value of B:")
    e1=Entry(new_frame, textvariable=var_a)
    e2=Entry(new_frame, textvariable=var_b)
    submit=Button(new_frame, text="Submit", fg="red", command=ans_c)

    label_a.grid(row=0, sticky=W)
    label_b.grid(row=1, sticky=W)
    e1.grid(row=0, column=1)
    e2.grid(row=1, column=1)
    submit.grid(row=2, column=1)




# Calls the initial welcome screen
start()
root.mainloop()

Answer 1

As few clicks as possible

If the user uses this programs he is not interested in clicking many buttons, he wants to know the result of the pythagoras theorem.

It would be more user friendly to show 3 labels, two for catets and one one for the hypothenusas and a single calculate button.

When the user presses the calculate button, the programme automatically detects which field is blank and proceeds to calculate its value. It is also possible to use it more times without closing and reopening.

Handle errors gently

Also please don't crash with a MathDomainError, catch the exception and show a messagebox saying "Triangle can't have negative catet" or "hypotenusas must be longer than cathet".