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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

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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

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
Answer:

For 30 60 90 triangles, the ratio of the side lengths is
 \frac{1}{2} : \frac{ \sqrt{3} }{2} :1
where the first is the shorter leg, the second is the longer leg, and the third is the hypotenuse (the longest side that doesn't form a 90 degree angle)

so the ratio of the longer leg to the hypotenuse is \frac{ \sqrt{3} }{2} :1
or
 \frac{ \frac{ \sqrt{3} }{2} }{1}
which equals  \frac{ \sqrt{3} }{2}

That is the answer 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

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