Question

question 5 of 10 which of the following are true statements about a 30 - 60 - 90 triangle? check all that apply. a. the longer leg is twice as long as the shorter leg. b. the hypotenuse is √3 times as long as the longer leg. c. the hypotenuse is twice as long as the shorter leg. d. the hypotenuse is √3 times as long as the shorter leg. e. the longer leg is √3 times as long as the shorter leg. f. the hypotenuse is twice as long as the longer leg.

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratios

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

Step2: Analyze each option

A is false. B is false. C is true as hypotenuse = $2x$ when shorter leg = $x$. D is false. E is true as longer leg = $\sqrt{3}x$ when shorter leg = $x$. F is false.

Answer:

C. The hypotenuse is twice as long as the shorter leg., E. The longer leg is $\sqrt{3}$ times as long as the shorter leg.