Question

question 1 of 10
which of the following could be the ratio between the lengths of the two legs of a 30 - 60 - 90 triangle?
check all that apply.
a. $sqrt{3}:sqrt{3}$
b. $sqrt{2}:sqrt{2}$
c. $1:sqrt{2}$
d. $2sqrt{3}:6$
e. $sqrt{2}:sqrt{3}$
f. $1:sqrt{3}$

Explanation:

Step1: Recall 30-60-90 triangle leg ratio

Legs ratio: \(1 : \sqrt{3}\) (shorter:longer)

Step2: Analyze each option

A: \(\sqrt{3}:\sqrt{3}=1:1\) (not 1:\(\sqrt{3}\))
B: \(\sqrt{2}:\sqrt{2}=1:1\) (not 1:\(\sqrt{3}\))
C: \(1:\sqrt{2}\) (not 1:\(\sqrt{3}\))
D: \(2\sqrt{3}:6=\sqrt{3}:3=1:\sqrt{3}\) (matches)
E: \(\sqrt{2}:\sqrt{3}\) (not 1:\(\sqrt{3}\))
F: \(1:\sqrt{3}\) (matches)

Answer:

D. \(2\sqrt{3} : 6\), F. \(1 : \sqrt{3}\)