In rhombus ABCD, AB=10 and the measure of angle ABC=120°. Find BD.

Using the side length as the hypotenuse of a right triangle and half the given angle as the adjacent angle. Find the length of the base of a right triangle. This would be half the length of BD.

Cos (60) = adjacent leg / 10

adjacent leg = cos (60) x 10

Adjacent leg = 5

Length of BD = 5x 2 =

10