Question

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

Answer 1

C and D are both correct.

The basic value is $\sqrt{3}$ : 2. The D values are twice that much. 

Answer 2

Answer:

The ratio of a longer leg and the hypotenuse is $\dfrac{\sqrt 3}{2}$

Step-by-step explanation:

The general length of the sides of 30-60-90 triangles is given below with the help of a diagram.

The length of the longest side is $2x.$

The length of a larger side is $\sqrt{3} x$

The length of a smaller side is $x$

Therefore,

The ratio of a longer leg and the hypotenuse can be calculated as:

$\begin{aligned}\dfrac{\rm{Longer\;leg}}{\rm{Hypotenuse}}&=\dfrac{\sqrt3 x}{2x}\\&=\dfrac{\sqrt 3}{2}\end{aligned}$

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