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]
