Question

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

Answer 1

Only option A (3:3√3) represents the correct ratio for the lengths of the legs in a 30-60-90 triangle, which can be simplified to 1:√3. The other options given do not correspond to the correct ratio.

Step-by-step explanation:

The question is asking for possible ratios of the lengths of the two legs of a 30-60-90 triangle. In a 30-60-90 triangle, the ratio of the lengths of the shorter leg to the longer leg (the one opposite the 60-degree angle) is always 1:√3. Therefore, we are looking for a ratio that simplifies to 1:√3.

• A. 3:3√3 - This simplifies to 1:√3 because both terms can be divided by 3.
• F. 1: √2 - This is not the correct ratio for a 30-60-90 triangle.

The other options (B, C, D, and E) are incorrect since they do not simplify to the correct ratio of 1:√3.