The sum of the two acute angles of a right triangle is $90^{\large\circ}$

Difference between the actute angles

$\large\frac{\pi}{15}^c=(\frac{\pi}{15}\times \frac{180}{\pi})^{\large\circ}$

$\Rightarrow 12^{\large\circ}$

Let the two acute angles be $x^{\large\circ}$ and $y^{\large\circ}$ then,

$x+y=90^{\large\circ}$--------(1)

$x-y=12^{\large\circ}$--------(2)

____________________

$2x=102^{\large\circ}$

$x=51^{\large\circ}$

$\Rightarrow y=39^{\large\circ}$

Hence the angles of a triangle are $51^{\large\circ},39^{\large\circ},90^{\large\circ}$

Hence (A) is the correct answer.