Find the value of x and the value of y.

x = 9*sqrt(3), y = 18

Step-by-step explanation:

There are special rules for 30,60,90 triangles, which these are, but I prefer just using trig or other properties.  If you need to know why these are 30,60,90, you just need to know that the sum of angles in a triangle are 180, and we know each triangle has a 90 degree angle and a 60 degree angle, so that just leaves 30.

For y it's actually super simple.  The two 30,60,90 triangles are one bigger triangle cut in half.  SPecifically an equilateral triangle since all three angles are the same.  Equilateral triangles have all three angles and sides equal to each other.  So since we know one side is 18 the other two are as well, so that means y = 18.

Since the equlateral triangle is getting cut in half we know the bottom side labeled ad 18 makes two sides each at a length of 9.  So nowwe have two right triangles  that have side lengths y, x, and 9.  We know y = 18, so we can use the pythagorean theorem to find x.  

x^2 + 9^2 = y^2

x^2 + 81 = 18^2

x^2 = 324 - 81

x = sqrt(243)

x = sqrt(81)*sqrt(3)

x = 9*sqrt(3)

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