Question

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

 

 

Answer 1

Given:
Difference between two acute angles of a right-angled triangle = \[\frac{2\pi}{5}\] rad  \[\because 1 \text{ rad }= \left( \frac{180}{\pi} \right)^\circ \]
\[\therefore \frac{2\pi}{5} rad = \left( \frac{180}{\pi} \times \frac{2\pi}{5} \right)^\circ\]
\[ = \left( 36 \times 2 \right)^\circ\]
\[ = {72}^\circ\]
Now, let one acute angle of the triangle be x°.
Therefore, the other acute angle will be 90° - x°.
Now,
\[x^\circ - \left( 90^\circ - x^\circ \right) = 72^\circ\]
\[ \Rightarrow x - 90 + x = 72\]
\[ \Rightarrow 2x = 162\]
\[ \Rightarrow x = 81\]
Thus, we have: x° = 81 and,
90° - x°
= 90° - 81°
=9°