Let's call the length of the rectangle "l" and the width "w". We know that the diagonal of the rectangle is 60 inches, and that it creates angles of 30 degrees and 60 degrees in the corners of the rectangle.
Using trigonometry, we can relate the sides of the rectangle to its diagonal and the angles formed by the diagonal. Specifically, we can use the sine and cosine functions to relate the sides to the angles:
sin(30) = w/60 and cos(30) = l/60
sin(60) = l/60 and cos(60) = w/60
Simplifying each equation, we get:
w = 30√3 and l = 30
Therefore, the area of the rectangle is:
Area = l x w = (30)(30√3) = 900√3 square inches.
Hence, the area of the rectangle in simplified radical form is 900√3 square inches.