The ratio of a longer leg of a 30-60-90 triangle to the length of its hypotenuse is C. sqrt 3: 2..
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
The length of the longest side = 2x
The length of a larger side = [tex]\sqrt{3x}[/tex]
The length of a smaller side = x
Therefore,
The ratio of a longer leg of a 30-60-90 triangle to the length of its hypotenuse can be calculated as:
[tex]\dfrac{ longer leg}{hypotenuse} = \dfrac{ \sqrt{3x} }{2x}\\\\= \dfrac{ \sqrt{3} }{2}[/tex]
So, the correct option is C. sqrt 3: 2.
Learn more about Pythagoras' theorem here:
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