Answer:
28.072°, 61.928°
Explanation:
You want the measures of the acute angles in a right triangle with sides 8, 15, 17.
Trig functions
Any of the (inverse) trig functions can be used to find the angles. You know the acute angles are complementary, so finding one tells you the measure of the other.
Tan = Opposite/Adjacent
The smallest angle (A) is adjacent to side 15 and opposite side 8.
tan(A) = 8/15
A = arctan(8/15) ≈ 28.072°
The complement is angle B:
B = 90° -28.072° = 61.928°
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Additional comment
We have taken sides {a, b, c} = {8, 15, 17}. The angles opposite those sides are A, B, C.
You can also use ...
A = arcsin(8/17)
B = arccos(8/17)