Consider a right triangle with hypotenuse of length \(61\) and one leg of length \(11\text{.}\) Let \(\alpha\) be the angle opposite the side of length \(11\text{.}\) Find the exact length of the other leg and then determine the value of each of the six trigonometric functions evaluated at \(\alpha\text{.}\) In addition, what are the exact and approximate measures of the two non-right angles in the triangle?