Sketch the following to help answer the question. Kite WXYZ has a short diagonal of XZ and a long diagonal of WY. The diagonals intersect at point V. The length of XZ = 8 cm, and the measure of ∠XYV is 30 degrees. Find the length of segment VY.

A kite is a 4-sided flat shape with straight sides. This figure has two pair sides. Each pair is made of two adjacent sides that are equal in length. This is shown in the figure below. As indicated the lengths in red are equal and the same happens with the lengths in blue. 

Given that diagonals (dashed lines) cross at right angles, and one of the diagonals bisects (cuts equally in half) the other, then it is true that:

[tex]\overline{xv}=\frac{\overline{xz}}{2}=4cm[/tex]

Therefore, using trigonometry:

[tex]\overline{vy}:Adjacent \ side \ (A) \\ \overline{xv}:Opposite \ side \ (O) \\ \\ H=\frac{O}{sin(30^{\circ})}=\frac{4}{sin(30^{\circ})}=8cm \\ \\ \overline{vy}=Hcos(30^{\circ})=8cos(30^{\circ}) \ \rightarrow \boxed{\overline{vy}=6.928cm}[/tex]