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.
A. 2 √3 : 4
B. √3 : √3
C. √3 : 2
D. 1 : √3
E. 2: 2 √2
F. √2: √3

Answer 1

The 3 values in ascending order are: 1,sqrt3,2
shorter leg would be 1
longer leg would be sqrt 3
hypotenuse would be 2
So longleg/hypot = sqrt3/2 or sqrt3:2

Answer 2

So choice C and F?

Answer 3

http://www.regentsprep.org/regents/math/algtrig/att2/ltri30.htm

Answer 4

So just c?

Answer 5

Only C

Answer 6

notice that in a ratio, if you multiply both the top and bottom , we get a similar ratio
for example
\[ \frac{\sqrt{3}}{2} = \frac{2\sqrt{3}}{4}\]
in other words, choice A is also a possible ratio of long side to hypotenuse in a 30-60-90 triangle

Answer 7

A good point phi, the choices of both A and C were presented, wonder how the instructor would have treated an answer of A ??

Answer 8

radar I believe that would also be correct for the instructor, because it says check all that apply.