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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

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MissPhiladelphia
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!
boffeemadrid

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 the diagonals are the perpendicular bisectors of each other, therefore [tex]XZ=ZV+VX[/tex]⇒[tex]ZV=VX=4 cm[/tex].

Now, from ΔVXY using trigonometry, we get

[tex]\frac{XV}{VY}=tan30^{\circ}[/tex]

Substituting the given values, we get

[tex]\frac{4}{VY}=\frac{1}{\sqrt{3}}[/tex]

[tex]VY=4\sqrt{3} cm[/tex]

Therefore, the length of the segment VY is [tex]4\sqrt{3} cm[/tex].

Hence, option D is correct.

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