Final answer:
In triangle ABC, with BC = 6 cm, CD perpendicular to AB, and angles ABC = 90 degrees and ACD = 60 degrees, AD can be found using trigonometric ratios. By applying sine, we can calculate that AD is equal to 3√3 cm.
Step-by-step explanation:
In triangle ABC, BC is 6 cm, CD is perpendicular to AB, angle ABC is 90 degrees, and angle ACD is 60 degrees. We are asked to find AD.
Since angle ABC is 90 degrees and CD is perpendicular to AB, triangle ABC is a right triangle.
By using trigonometric ratios, we can find the length of AD. The sine of angle ACD is equal to the length of the side opposite to it (AD) divided by the length of the hypotenuse (AC).
Sin(60 degrees) = AD/6 cm => AD = 6 cm * sin(60 degrees) => AD = 6 cm * (√3/2) => AD = 3√3 cm.