Question

Which of the following could be the ratio length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse

Answer 1

Answer:

$\sqrt{3} : 2$

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) = $x$ units, then one leg of the Δ will be $x*cos30$ units (AC) = $\frac{\sqrt{3} }{2} *x$ units and the other leg will be $x * sin30$ units (BC) =$\frac{x}{2}$ units.

Here the length of longer leg (AC) = $\frac{\sqrt{3} }{2} *x$ units and the length of hypotenuse = $x$ units.

Hence the ratio of the length of longer leg and the length of the hypotenuse in the Δ = AC:AB = $\frac{\sqrt{3} }{2} *x:x$ =$\frac{\sqrt{3} }{2}$

Answer 2

The sides of a 30-60-90 triangle have the ratios 1:√3:2. The ratio of the longest side to the hypotenuse is
  (√3)/2