skyolivera05
Answered

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What are the values of x and y?

Question 18 options:


A)


x = 8; y = 4


B)


x = 8[tex]\sqrt{3}[/tex] ; y = 4[tex]\sqrt{3}[/tex]


C)


x = 6[tex]\sqrt{x3}[/tex] ; y = 3[tex]\sqrt{3}[/tex]


D)


x = 4[tex]\sqrt{3}[/tex] ; y = 8[tex]\sqrt{3}[/tex]

What Are The Values Of X And YQuestion 18 OptionsA X 8 Y 4B X 8texsqrt3tex Y 4texsqrt3texC X 6texsqrtx3tex Y 3texsqrt3texD X 4texsqrt3tex Y 8texsqrt3tex class=

Sagot :

clarch19

Answer:

B)   x = 8[tex]\sqrt{3}[/tex] ;  y = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

in a 30-60-90° triangle the sides, respectively, are in the ratio of

1 : [tex]\sqrt{3}[/tex] : 2

we can find 'x' by creating this proportion:

12/[tex]\sqrt{3}[/tex] = x/2

cross-multiply to get:

[tex]\sqrt{3}[/tex]x = 24

x = 24/[tex]\sqrt{3}[/tex]

we can simplify this by 'rationalizing the denominator' which is to

multiply numerator and denominator by [tex]\sqrt{3}[/tex] to get:

(24[tex]\sqrt{3}[/tex])÷3, which is 8[tex]\sqrt{3}[/tex]

we know that side 'y' is half that of side 'x'

therefore y = 4[tex]\sqrt{3}[/tex]

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