When you have a right triangle (A triangle which has a angle of 90°), you can find the "Sine". This is one of the basi trigonometric ratios. By definition, the Sine is:
Sin(α)=Opposite leg/Hypotenuse
You want to find Sin(A), so the opposite leg will be 8√3 and the hypotenuse will be 16.
When you substitue these values, you have:
Sin(α)=Opposite leg/Hypotenuse
Sin(A)=8√3/16
When you simplify, you obtain:
Sin(A)=4√3/8
Sin(A)=2√3/4
Sin(A)=√3/2
Which is the ratio for Sin(A)?
The answer is: The ratio for Sin(A) is √3/2