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.

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