I was approved for disability and was sent a large backpay disability check. Must I pay taxes on this check amount and if so how much?

There isn't a simple Yes or No answer.
If the disability payments are from a private policy that you made premium contributions to (not part of a State program or entirely funded by employer plan), than the payments are NOT taxable income.

Refer to IRS Publication 525.

Indian CPA
Home - Indian CPA (http://www.indiancpa.com)

If this is US Social Security Disability, you must include that lump sum in your calculations. Whether you will owe or not depends on factors such as total income, single/married, and whether you take the lump sum election for benefits covering the previous year, which may or may not mean a lower tax. If you feel anonymous you can say all that here, but I wouldn't if this ID is your real name.