Question

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

Answer 1

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

Answer 2

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

Answer 3

6.93