Let
x---------> the measure of the angle opposite the leg that is 6 inches long
we know that
tan x=opposite side angle x/adjacent side angle x
opposite side angle x------> 6 in
adjacent side angle x-------> 6√3 in
so
tan x=6/(6√3)-----> x=1/√3------> √3/3
x=arc tan(√3/3)------> x=30°
the answer is
30°
