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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

User Volex
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2 Answers

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Answer:

its not right i got it wrong

Explanation:

User Cornish
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6 votes
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:

(1)/( √(3) ) =XV/VY \\ VY= √(3) *XV=4 √(3) cm
User RanH
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