The hypotenuse of a right triangle measures 3sqrt(15) centimeters and its shorter leg measures 3sqrt(6) centimeters. What is the measure of the larger acute angle of the triangle? Round your answer to the nearest tenth of a degree. Please help and explain. No links or stealing points please.

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.