Answer:
x = 4[tex]\sqrt{3}[/tex]
y = 8[tex]\sqrt{3}[/tex]
Step-by-step explanation:
this is a 30-60-90 triangle and the sides have a constant ratio
the side across from the 30°∡ is 1
the side across from the 60°∡ is √3
the side across from the 90°∡ is 2
In this problem we can find 'x' by setting up this proportion:
x/12 = [tex]\sqrt{3}[/tex]/1
cross-multiply:
[tex]\sqrt{3}[/tex]x = 12
x = 12/[tex]\sqrt{3}[/tex]
since we don't like to leave radicals in the denominator, we can multiply both numerator and denominator by [tex]\sqrt{3}[/tex] to get:
12[tex]\sqrt{3}[/tex] ÷ [tex]\sqrt{3}[/tex]·[tex]\sqrt{3}[/tex] ([tex]\sqrt{3}[/tex]·[tex]\sqrt{3}[/tex] = [tex]\sqrt{9}[/tex], which equals 3)
so we have 12[tex]\sqrt{3}[/tex]/3, which is 4[tex]\sqrt{3}[/tex]
The 'y' value will be twice the 30° side, so 8[tex]\sqrt{3}[/tex]
