Question

If the sides of a right angled triangle are in arthmetic progression then the sines of acute angles are

Answer 1

Let the sides be  b-d,  b  and b+d.  
The common difference is d.  Hypotenuse is b+d.

Since it is a right angle triangle, 
      
             b² + (b-d)² = (b+d)²
             2 b² + d² - 2 b d  =  b² + d² + 2 b d
              b² = 4 b d 
                   b = 4 d 
      So the sides are :    3d , 4d,   and    hypotenuse is   5d
 
  Hence the angles are :  Sin 3/5  and  Sin 4/5