Final answer:
To find the length of the diagonals AC and BD of the given rhombus ABCD, we can use trigonometry. The length of diagonal AC is 8 * sqrt(3).
Step-by-step explanation:
To find the length of the diagonals AC and BD of the given rhombus ABCD, we can use trigonometry. Since angle ACB is 120 degrees, we can use the law of cosines to find the length of AC or BD. Let's assume AC is the diagonal we want to find. We have:
AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(ACB)
AC^2 = 8^2 + 8^2 - 2 * 8 * 8 * cos(120)
Simplifying, we get:
AC^2 = 64 + 64 - 128 * cos(120)
AC^2 = 128 - 128 * (-0.5)
AC^2 = 128 + 64
AC^2 = 192
Taking the square root of both sides, we get:
AC = sqrt(192)
AC = sqrt(64 * 3)
AC = 8 * sqrt(3)
So, the length of diagonal AC is 8 * sqrt(3).