Final answer:
To find AD, we can use trigonometry and the properties of a 30-60-90 triangle given the information provided. We can determine that AD is equal to 6 cm.
Step-by-step explanation:
To find AD, we can use the trigonometric relationship between the sides and angles in a right triangle. Since triangle ABC is a right triangle with angle ACB = 90 degrees, we can use the trigonometric function cosine to relate the side lengths. In particular, we can use the cosine of angle ACB to find the length of AD.
Since m ACD = 60 degrees and m ACB = 90 degrees, the remaining angle in triangle ACD is 180 - 60 - 90 = 30 degrees. Therefore, triangle ACD is a 30-60-90 triangle.
In a 30-60-90 triangle, the ratio between the sides is 1:sqrt(3):2. Since BC = 6 cm, we can use the ratio to determine the length of AD. The ratio tells us that AD = 2 * CD and CD = BC / 2 = 6 / 2 = 3 cm. Therefore, AD = 2 * 3 = 6 cm.