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]
