Question:
The difference between the two acute angles of a right triangle is $\left(\frac{\pi}{5}\right)^{\mathrm{c}}$
Solution:
The angle in degree $=\frac{\pi}{5} \times \frac{180}{\pi}=36^{\circ}$
$=36^{\circ}$
Let, two acute angles are x and y
So,
ATQ, $x-y=36^{\circ} . .$
$x+y=90^{\circ} \ldots \ldots(2)$
Solving 1 & 2, we get;
$\Rightarrow 2 x=126^{\circ}$
$\Rightarrow x=63^{\circ}$
Putting the value of x in 2, we get;
$\Rightarrow 63^{\circ}+y=90^{\circ}$
$\Rightarrow y=27^{\circ}$
So, Two acute angles are $63^{\circ} \& 27^{\circ}$