Question

question 4 of 10 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. 2:2√2 b. 2√3:4 c. √2:√3 d. 1:√3 e. √3:√3 f. √3:2

Explanation:

Step1: Recall 30-60-90 triangle ratios

Sides: shorter leg : longer leg : hypotenuse = 1 : √3 : 2. Thus, longer leg : hypotenuse = √3 : 2.

Step2: Simplify each option

• A: 2:2√2 = 1:√2 ≠ √3:2
• B: 2√3:4 = √3:2 ✔️
• C: √2:√3 ≈1.414:1.732 ≠ √3:2
• D: 1:√3 (shorter:longer) ≠ √3:2
• E: √3:√3=1:1 ≠ √3:2
• F: √3:2 ✔️

Answer:

B. 2√3 : 4, F. √3 : 2