Ugly problem that works out nicely

Geometry Level pending

The current year is 2016. The last year number which was a perfect square was 1936 and before that, 1849.

If \(\theta =\log _{ \sqrt [ 30 ]{ 45 } }{ x } \) (logarithim with base \(\sqrt [ 30 ]{ 45 } \)) in degrees, where \(x\) is the next perfect-square year number, then the area of the triangle below can be written as \(\frac { a\sqrt { b }}{ c } \), where \(a\), \(b\), and \(c\) are positive integers, with \(a\) and \(c\) being coprime integers and \(b\) square-free.

What is \(a+b+c\)?

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