Question

question 5 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. \\(\sqrt{3} : 2\\)
b. \\(1 : \sqrt{3}\\)
c. \\(2 : 2\sqrt{2}\\)
d. \\(\sqrt{3} : \sqrt{3}\\)
e. \\(\sqrt{2} : \sqrt{3}\\)
f. \\(2\sqrt{3} : 4\\)

Explanation:

Identify side length relationships

Using the 30-60-90 Triangle Properties knowledge point

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Determine target ratio

Using the 30-60-90 Triangle Properties knowledge point

$$ \text{Ratio} = \frac{\text{Longer leg}}{\text{Hypotenuse}} = \frac{x\sqrt{3}}{2x} = \frac{\sqrt{3}}{2} $$

Evaluate given options

Using the 30-60-90 Triangle Properties knowledge point

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Answer:

• (A) \(\sqrt{3} : 2\) (Correct answer)
• (B) \(1 : \sqrt{3}\)
• (C) \(2 : 2\sqrt{2}\)
• (D) \(\sqrt{3} : \sqrt{3}\)
• (E) \(\sqrt{2} : \sqrt{3}\)
• (F) \(2\sqrt{3} : 4\) (Correct answer)