# The difference between the two acute angles of a right-angled triangle is

Question:

The difference between the two acute angles of a right-angled triangle is $\frac{2 \pi}{5}$ radians. Express the angles in degrees.

Solution:

Given:

Difference between two acute angles of a right-angled triangle $=\frac{2 \pi}{5} \mathrm{rad}$

$\because 1 \mathrm{rad}=\left(\frac{180}{\pi}\right)^{\circ}$

$\therefore \frac{2 \pi}{5} \mathrm{rad}=\left(\frac{180}{\pi} \times \frac{2 \pi}{5}\right)^{\circ}$

$=(36 \times 2)^{\circ}$

$=72^{\circ}$