To calculate Kyrian's total cost, we first need to calculate the tip amount and then add it to the original cost of the haircut.
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Calculate 20% of $13.99: \[ \text{Tip} = 0.20 \times 13.99 = 2.798 \]
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Round the tip to the nearest hundredth: \[ \text{Rounded Tip} = 2.80 \]
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Add the tip to the original cost of the haircut: \[ \text{Total Cost} = 13.99 + 2.80 = 16.79 \]
So the total cost rounded to the nearest hundredth is $16.79.