If the acute angles in a right triangle are in the ratio of 5:4 find the measure of the smallest angle

Let's create this right triangle. We will call it triangle ABC with angle B as the right angle, angle A being the larger of the angles A and C. If the ratio is 5:4, then it is A:C. 5+4 = 9. The measure of the right angle, angle ABC = 90, and 90 divided by 9 is 10. So angle A is 5 * 10 which is 50 degrees, and angle C is 4 * 10 which is 40 degrees. The smallest angle, angle C, is 40 degrees.