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

Answer 1

(D)

Explanation:

It is given that 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°.

We know that the diagonals are the perpendicular bisectors of each other, therefore
`XZ=ZV+VX`⇒
`ZV=VX=4 cm`.

Now, from ΔVXY using trigonometry, we get

`(XV)/(VY)=tan30^(\circ)`

Substituting the given values, we get

`(4)/(VY)=(1)/(√(3))`

`VY=4√(3) cm`

Therefore, the length of the segment VY is
`4√(3) cm`.

Hence, option D is correct.

Answer 2

The best and most correct answer among the choices provided by the question is the first choice. Based on my calculations, the length of segment Vy is 16 cm. I hope my answer has come to your help. God bless and have a nice day ahead!