trig question

Since no one else has posted an answer, I'll post what I have ...

 

Using 'a' as the side opposite angle(A), 'b' as the side opposite angle(B), and 'c' as the side opposite angle(C):

 

Since angle(B) is a right angle:  sin(A) = a/b     cos(A) = c/b     tan(A) = a/c     b² = a² + c²

 

sin(A)  =  2·cos(A) + tan(A)     --->     a/b  =  2(c/b) + a/c

          multiplying by  bc          --->      ac  =  2c² + ab

 

Solving for  c  by using the quadratic formula:  ac  =  2c² + ab

                                                         2c² - ac + ab  =  0

                                c  =  [ a +/- sqrt( a² - 8ab ) ] /4

 

Since the answer is a real number:  a² - 8ab  >= 0

                                                                   a²  >=  8ab

 

Since  a  must be positive:                         a  >=  8b

        

which means that  a  must be larger than  b  but  b  is the hypotenuse!

 

So, either the problem, as stated, is impossible or I messed up!  Help!