Help me? Show work so I can understand please and thank you!

I think this is correct, Answer is 21
Step-by-step explanation:
Step 1: Write down formula: [tex]a^2+b^2+c^2[/tex]
Step 2: Plug in b and c value in formula: [tex]a^2+20^2=29^2[/tex]
Step 3: Solve the exponents: [tex]a^2+400=841[/tex]
Step 4: Subtract 400 from both sides: [tex]-400[/tex] [tex]-400[/tex]
[tex]a^2=441[/tex]
Step 5: Square root both sides: [tex]\sqrt{a^2}=\sqrt{441}[/tex]
[tex]a=21[/tex]
Step 6: 29+21: 50
Step 7: 50-29: 21