Question 1009190
In such a 30-60-90 right triangle, the side opposite the 30 degree angle is half the hypotenuse.  That side is BC here.  So if we call the hypotenuse AB, x, then
(1/4)x + 5 = (1/2)x
5 = (1/4)x
x = 20 = AB
BC = 10 and
AC, the longer leg, is 10*sqrt(3).