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Beach House Depreciation and Eventual Recapture

We are looking at buying a house at the beach.  We will plan on using it much more than 10%. Lets say  we will use it 126 days and it will be rented at FMV 84 days.    (60/40)  .

 

Let's also say that house cost $375K and the the non-land basis is $275,000 .  
And finally, we'll say that the incoming rental income will be 25K - just rental mgmt expenses = 20K.

The first Q is, do we get to depreciate the house, an if so, by what amount . 
Lets say we sell the home 10 years later at a price of $500K, on what amount would we pay taxes.

There will be a follow on Q, but I want to get this straight first .