Question

Which of the the following could be the ratio between the lengths of the two legs of a 30-60-90?Check all that apply.                                                                                                (A)Sqrt2:Sqrt3 (B)1:Sqrt2 (c)Sqrt2:Sqrt2 (D)2Sqrt3:Sqrt6 (E)1:Sqrt3 (F)Sqrt3:Sqrt3

Answer 1

`(a)/(a √(3) ) = (1)/( √(3) ) \ \ \ \Rightarrow\ \ \ Ans.\ E\\\\(2a)/(a √(3) ) = (2)/( √(3) )=(2\cdot √(2) )/( √(3)\cdot √(2) )=(2 √(2) )/( √(6) ) \\eq (2 √(3) )/( √(6) ) \\\\ (a)/(2a ) = (1)/( 2 )`

Answer 2

This is worth remembering:

In a 30-60-right triangle,
-- the side opposite the 30 is 1/2 the hypotenuse
-- the side opposite the 60 is (1/2 the hypotenuse) times (square root of 3).

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I believe Choice-'E' is the only one you could make with the above rule.