Final answer:
After applying the Law of Cosines to triangle ABC, the calculated length for side BC is approximately 6.87 cm, which does not match any of the provided answer options.
Step-by-step explanation:
To determine the length of side BC in triangle ABC, where AB = 6 cm, ∠BAC = 60 degrees, and AC = 7.5 cm, we can use the Law of Cosines. This law relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we can set up the equation:
BC^2 = AB^2 + AC^2 - 2(AB)(AC)cos(∠BAC).
Plugging in the values we have:
BC^2 = 6^2 + 7.5^2 - 2(6)(7.5)cos(60°)
BC^2 = 36 + 56.25 - 2(6)(7.5)(0.5)
BC^2 = 36 + 56.25 - 45
BC^2 = 92.25 - 45
BC^2 = 47.25
BC = √47.25
BC ≈ 6.87 cm
Therefore, none of the options provided (A, B, C, D) matches with the calculated length of side BC.