What is the measure of the other acute angle in the triangle?

Remember that the sum of the three angles of a triangle is always 180 degrees. Also, that the measure of a right angle is always 90 degrees. Therefore, as possessing a right angle is the defining characteristic of a right triangle, we already know the measures of two angles:

90 deg + 56-2/3 deg + angle C = 180 deg

Now, simply use an algebraic process to find the measure of the unknown acute angle. Add the measures of the two known angles & subtract that sum from 180 degrees. That is your solution!

By the way, the word "acute" in this problem is frivolous, as a right angle always has one right angle & two acute angles (angles of less than 90 degrees). It is impossible for any right angle to contain an "obtuse" angle (more than 90 degrees) or more than one right angle (angle of 90 degrees).