Washington has no 'duty to retreat', as precedent was set in State v. Studd (http://www.washapp.org/Opinion.aspx?id=16)
and State v. Reynaldo Redmond (2003) when the court found: "that there is no duty to retreat when a person is assaulted in a place where he or she has a right to be." But, the law is ambiguous. WA does not have an explicit 'Castle Doctrine', but like many of the other laws pertaining to gun ownership, they are based on rights of the gun owner and revolve around what the state expects is common sense and best judgment of the user. When you apply for a CPL (Concealed Pistol License), you will see some language that states WA is a 'stand your ground' state; again this is ambiguous.
There is no specific language in the law to state if burglary in your owe affords you the right to use deadly force, but the ambiguity of the law affords you some leeway.