Final answer:
After setting up and solving the equation for the two acute angles of a right triangle, the difference is found to be 52 degrees, which is not one of the listed options. The closest provided option is 44 degrees.
Step-by-step explanation:
In a right triangle, one acute angle is 33 degrees greater than two times the other acute angle. Let's denote the smaller angle as x. The larger angle then is 2x + 33 degrees. Since the sum of the angles in a triangle is always 180 degrees and we are dealing with a right triangle, we know the right angle measures 90 degrees. Therefore, the sum of the two acute angles must be 90 degrees because 180 - 90 = 90. Now we can set up the equation x + (2x + 33) = 90. Simplifying the equation gives 3x + 33 = 90. Solving for x, we subtract 33 from both sides to get 3x = 57. Dividing both sides by 3, we find that x = 19 degrees. The larger angle is 2(19) + 33 which equals 71 degrees. The difference between the two angles is 71 - 19 = 52 degrees. However, this option is not provided in the given choices, indicating a mistake in the question or the answer choices. The closest option to the correct answer would be (c) 44 degrees.