Question

question 6 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\sqrt{2} b. \sqrt{3}:\sqrt{3} c. 2\sqrt{3}:4 d. \sqrt{2}:\sqrt{3} e. 1:\sqrt{3} f. \sqrt{3}:2

Explanation:

Step1: Recall side - length ratio

In a 30 - 60 - 90 triangle, if the shorter leg is $a$, the longer leg is $a\sqrt{3}$ and the hypotenuse is $2a$. So the ratio of the longer leg to the hypotenuse is $\sqrt{3}:2$.

Step2: Simplify options

Simplify each option to see if it equals $\sqrt{3}:2$.

• Option A: $2:2\sqrt{2}=\sqrt{2}:2$ (divide by 2).
• Option B: $\sqrt{3}:\sqrt{3} = 1:1$.
• Option C: $2\sqrt{3}:4=\sqrt{3}:2$ (divide by 2).
• Option D: $\sqrt{2}:\sqrt{3}$.
• Option E: $1:\sqrt{3}$.
• Option F: $\sqrt{3}:2$.

Answer:

C. $2\sqrt{3}:4$, F. $\sqrt{3}:2$