In the above figure, what is the length of \(\overline{AB}\) in terms of \(a?\)

(A) \(\ \ a\sqrt{3}\)

(B) \(\ \ 2a\)

(C) \(\ \ a + \sqrt{3}\)

(D) \(\ \ a + a\sqrt{2}\)

(E) \(\ \ a+a\sqrt{3}\)

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