The difference between the two acute angles of a right-angled triangle is 2π/5 radians. Express the angles in degrees.

Question

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

Answer 1

Given the difference between the two acute angles of a right-angled triangle is \(\frac{2π}5\) radians. 

We know that π rad = 180° 

⇒ 1 rad = \(\frac{180°}π \)

Given  \(\frac{2π}5 \)

= 72° 

Let one acute angle be x° and the other acute angle be 90° - x°. 

Then, 

⇒ x° - (90° - x°) = 72° 

⇒ 2x° - 90° = 72° 

⇒ 2x° = 72° + 90° 

⇒ 2x° = 162° 

⇒ x° = 162°/ 2 

∴ x° = 81° and 90° - x° = 90° - 81° = 9°