Sketch the following to 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 = 8cm, and the measure of ∠xyv is 30 degrees. find the length of segment vy. 16cm 8√3cm 8cm 4√3cm

In a kite, the diagonals intersect normally. Hence, we also know that XV= 4cm, half of XZ. This is because the triangle XVY and XVW are equal, but it is a general property of kitest. XVY is the right angle in this. We can use then trigonometry to calculate VY.
We have that tan30= opposite site of angle XYV/adjacent leg by the definition of the tangent. Hence tan30= XV/YV. Thus, substituting the value of the tangent: