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

Answer 1

In a 30-60-90 triangle, the correct ratios between the lengths of the two legs (shorter to longer) are 1:√3 and any equivalent ratio, such as 3:3√3 after simplification. Options B and C are the only correct choices from the ones provided.

Step-by-step explanation:

In a 30-60-90 triangle, the length of the hypotenuse is twice that of the shorter leg, and the length of the longer leg is sqrt(3) times the shorter leg. Therefore, the ratio of the lengths of the two legs (shorter to longer) is 1:√3. From the options given:

• B. 1:√3 is correct because it follows the ratio of the sides in a 30-60-90 triangle.
• C. 3:3√3 is correct because when you simplify the ratio by dividing both sides by 3, you get 1:√3, which is the same as option B, thus it is also a correct ratio.

Options A, D, and E do not represent the ratio between the lengths of the two legs in a 30-60-90 triangle and are, therefore, incorrect.