trignometry
posted by gt .
In the right triangle shown below, the length of AB is 8 units, ¡ÏA measures 60¡ã, sin 60¡ã ¡Ö 0.866,
cos 60¡ã ¡Ö 0.5, and tan 60¡ã ¡Ö 1.73. Approximately how many units long is BC , to the nearest
hundredth of a unit?
A. 4.00

Since you posted this twice, I think you realized that the symbols did not come out like you intended.
I think you meant this:
AB = 8, angle A = 60°
then you are given
sin60° = .866
cos60° = .5
tan60° = 1.73
the problem is that we don't know where the 90° angle is, could be at C or at B
If angle B = 90°
then
BC/8 = tan60
BC = 8tan60 = 8(1.732) = appr 13.86
if angle C = 90°
then
BC/8 = sin60
BC = 8sin60 = 8(.866) = appr 6.93 
If it helps the answer according to this ACT compass sample test questions print out is 6.93.
How to solve it is the question ...
C is a 90 degree angle.
AB is 8 and the hypotenuse.
AC is the base .... we don't know it's length.
It's on page 14 if you google this 
2014 ACT In the right triangle shown below, the length of AB is 8 units