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

`√(3) : 2`

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) =
`(√(3) )/(2) *x` units and the other leg will be
`x * sin30` units (BC) =
`(x)/(2)` units.

Here the length of longer leg (AC) =
`(√(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 =
`(√(3) )/(2) *x:x` =
`(√(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