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

Answer:

(D)

Step-by-step 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

$\frac{XV}{VY}=tan30^{\circ}$

⇒$\frac{4}{VY}=\frac{1}{\sqrt{3}}$

⇒$VY=4\sqrt{3}cm$

Therefore, the length of the segment VY is $4\sqrt{3}cm$.

Answer 2

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)