ABCD is a rhombus of side 10 cm in which angle ABC = 120°. What is the length of the diagonal AC?

The diagonals of a rhombus bisect its angles and cross at right angles. Let them meet at O. Then angle ABO = 120°/2 = 60° and angle AOB = 90°, so triangle AOB is a 30°–60°–90° triangle with hypotenuse AB = 10. The side opposite the 60° angle is AO = 10 × (√3/2) = 5√3, and AC = 2 × AO = 10√3 cm (about 17.3 cm). The trap 10 cm is the other diagonal BD, since triangle ABD is equilateral.