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Choice B is correct. The sum of the measures of the interior angles of a triangle is $180$ degrees. Since the triangle is a right triangle, it has one angle that measures $90$ degrees. Therefore, the sum of the measures, in degrees, of the remaining two angles is $180-90$, or $90$. It’s given that the measure of one of the acute angles in the triangle is $51$ degrees. Therefore, the measure, in degrees, of the other acute angle is $90-51$, or $39$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the measure, in degrees, of the acute angle whose measure is given.