Answer:
x = [tex]\frac{8}{3}[/tex][tex]\sqrt{3}[/tex]
Step-by-step explanation:
in a 30-60-90 triangle the ratio of the side lengths is 1 : 2 : [tex]\sqrt{3}[/tex]
to find the length of short leg, x, you can create this proportion:
x / 8 = 1 / [tex]\sqrt{3}[/tex]
cross-multiply to get:
[tex]\sqrt{3}[/tex] x = 8
x = 8 / [tex]\sqrt{3}[/tex]
rationalize the denominator by multiplying numerator and denominator by [tex]\sqrt{3}[/tex]
x = [tex]\frac{8}{3}[/tex][tex]\sqrt{3}[/tex]
