Question

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 = 8cm, and the measure of ∠XYV is 30 degrees. Find the length of segment VY.

16cm
8√3cm
8cm
4√3cm

Answer 1

XV = 8 cm and angle XYV = 30

Tangent (XYV) = XV / VY
Tangent (30) = 4 cm / VY
VY = 4 cm / 0.57735
VY = 6.9282064606 cm

= 4 * square root (3)

Answer 2

(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, in Kite, the diagonals are the perpendicular bisectors, therefore ∠V=90° and XZ=8⇒XV=4cm

Now, from ΔXVY, we have

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

⇒
`(4)/(VY)=(1)/(√(3))`

⇒
`VY=4√(3)cm`

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