The diagram shows a triangle ABC with AC = 6 cm, BC = 8 cm, angle BAC = 60° and angle ABC = 𝛾. Find the exact value of sin⁡𝛾, simplifying your answer.

To find the exact value of sin𝛾, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

Here's how we can apply it:

1. We know that AC = 6 cm, BC = 8 cm, and ∠BAC = 60°. We want to find sin𝛾 where 𝛾 is ∠ABC.

2. According to the Law of Sines, we have:

   (BC/sin∠BAC) = (AC/sin∠ABC)

3. Substituting the given values, we get:

   (8/sin60°) = (6/sin𝛾)

4. Simplifying the left side (since sin60° = √3/2), we get:

   (8/(√3/2)) = (6/sin𝛾)

5. Further simplifying, we get:

   (16/√3) = (6/sin𝛾)

6. Cross-multiplying to solve for sin𝛾, we get:

   sin𝛾 = 6*(√3/16)

7. Simplifying, we get:

   sin𝛾 = √3/8

So, the exact value of sin𝛾 is √3/8.