Question 191742
draw  triangle  abc

a=30deg,   c=90  deg,  therefore  b=60  deg   (sum  of  angles  =  180)

bc  =  .25 ab  +4     (given)

but  in  30-60-90  triangle,    bc  =  1/2  ab

therefore  ab  =  1/2  ab  +8

simplifying    1/2  ab  =  8

ab=16

subst  bc  =  .25  (16)  +4  =  8

using  pythagorous  

16^2  - 8^2  =  256 - 64 =  192 =  ac^2

ac =  (64  *3)^.5  =  8 *3^.5   or  8  sq rt  3

check   30-60-90  triangle  makes  1-2-sq rt 3  sides,  8-16-8sqrt3  ok