Question

question 6 of 10

which of the following are true statements about a 30-60-90 triangle?

check all that apply.

a. the hypotenuse is \\(\sqrt{3}\\) times as long as the shorter leg.
b. the hypotenuse is twice as long as the shorter leg.
c. the longer leg is \\(\sqrt{3}\\) times as long as the shorter leg.
d. the longer leg is twice as long as the shorter leg.
e. the hypotenuse is twice as long as the longer leg.
f. the hypotenuse is \\(\sqrt{3}\\) times as long as the longer leg.

Explanation:

Define the side ratios of a 30-60-90 triangle

Using the 30-60-90 Triangle Properties knowledge point

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Evaluate statements comparing hypotenuse and shorter leg

Using the 30-60-90 Triangle Properties knowledge point

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Evaluate statements comparing longer leg and shorter leg

Using the 30-60-90 Triangle Properties knowledge point

$$
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Evaluate statements comparing hypotenuse and longer leg

Using the 30-60-90 Triangle Properties knowledge point

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Answer:

• A. The hypotenuse is \(\sqrt{3}\) times as long as the shorter leg.
• B. The hypotenuse is twice as long as the shorter leg. (Correct answer)
• C. The longer leg is \(\sqrt{3}\) times as long as the shorter leg. (Correct answer)
• D. The longer leg is twice as long as the shorter leg.
• E. The hypotenuse is twice as long as the longer leg.
• F. The hypotenuse is \(\sqrt{3}\) times as long as the longer leg.