A portion of your long term capital gains will be taxed at 0% and the balance at 15%. Based on 2019 tax rates and standard deduction, if you are married filing jointly under the age of 65 and you take the standard deduction of $24,400, $35,600 of your $60,000 of ordinary income is taxable at ordinary income tax rates. You add your capital gains to your taxable ordinary income. When the sum of those two reaches $78,750, the portion of that amount from capital gains or $43,150 is taxed at 0%. The balance of $6,850 above $78,750 is taxed at 15%.
The tax rate on long-term capital gain is based on taxable income, not AGI. And it is based on total taxable income, including the capital gain. It also depends on your filing status, which you didn't specify. Since you said "we" I'll assume you are married filing jointly.
For 2020, if you are married filing jointly and you are both under 65 and not blind, your standard deduction will be $24,800. If your AGI, excluding the capital gain, is $60,000, and you take the standard deduction, your taxable ordinary income will be $35,200.
The long-term gain is "stacked" on top of your ordinary income for calculating the tax rate. So if you stack a $50,000 gain on top of $35,200 of ordinary taxable income, your total taxable income will be $85,200. For 2020, the top of the 0% bracket for long-term capital gain is $80,000. So your income straddles the 0% and 15% brackets. The first $44,800 of the gain will be taxed at 0%. Any gain over that amount ($5,200 in this example) will fall in the 15% bracket.