Question

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

Answer 1

The sum of the two acute angles of a right triangle is 90∘90∘

Difference between the actute angles

π15c=(π15×180π)∘π15c=(π15×180π)∘

⇒12∘⇒12∘

Let the two acute angles be x∘x∘ and y∘y∘ then,

x+y=90∘x+y=90∘--------(1)

x−y=12∘x−y=12∘--------(2)

____________________

2x=102∘2x=102∘

x=51∘x=51∘

⇒y=39∘

Answer 2

Answer:

• let the two acute angles be( x degree) & (90-x degree)
• A/q
• x-(90-x)=2pi/5 radians
• now convert 2pi/5 radian into degrees
• as we know that 1 radian=180/pi degree
• therfore,2pi/5 x 180/pi = 72 degree
• now x- 90 - x=72 degree
• 2x=90+72
• 2x=162
• x=81 degrees
• therefore 90-x= 90-81=9 degrees
• hope you understood the question.