Christmas Math Problem

Geometry Level 2

An elf is locked outside of Santa's workshop, and has forgotten the code to get back inside. Beside the door, there is a sign that says: "To get the code to the door, solve the following math problem:"

A right triangle has side lengths so the hypotenuse is equal to \(21\), and the length of one of the other sides is \(n\). If the equation, \(9n^2 - 279n + 2162.25=0\) holds true, then find the measures of the two other angles in this right triangle. If these two angles are labelled \(A\) and \(B\), where \(A\) is the angle that is opposite side \(n\), express your answer as \(\frac{A}{B}\), rounded to the nearest hundredth.

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