Answer:
[tex]\sqrt{3} : 2[/tex]
Step-by-step explanation:
We construct a ΔABC which is same a 30-60-90 triangle ( see in the figure).
Now, let be the length of hypotenuse (AB) = [tex]x[/tex] units, then one leg of the Δ will be [tex]x*cos30[/tex] units (AC) = [tex]\frac{\sqrt{3} }{2} *x[/tex] units and the other leg will be [tex]x * sin30[/tex] units (BC) =[tex]\frac{x}{2}[/tex] units.
Here the length of longer leg (AC) = [tex]\frac{\sqrt{3} }{2} *x[/tex] units and the length of hypotenuse = [tex]x[/tex] units.
Hence the ratio of the length of longer leg and the length of the hypotenuse in the Δ = AC:AB = [tex]\frac{\sqrt{3} }{2} *x:x[/tex] =[tex]\frac{\sqrt{3} }{2}[/tex]
