Which of the following are true statements about a 30-60-90 triangle? Check all that apply. A. The hypotenuse is twice as long as the longer leg. B. The longer leg is /3 times as long as the shorter leg. C. The hypotenuse is twice as long as the shorter leg. D. The longer leg is twice as long as the shorter leg. E. The hypotenuse is /3 times as long as the longer leg. F. The hypotenuse is /3 times as long as the shorter leg.

A 30-60-90 triangle is a right triangle with one leg equal to x, the other leg equal to 2x and the hypotenuse equal to x*sqrt(3). So, there you see that the longer leg is twice as long as the shorter leg (option D) and the hypotenuse is sqrt(3) times as long as the shorter leg (option F). Answer: the true statements are D. and F.

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FelisFelis FelisFelis · Answer 2 · 2019-11-26T06:37:44+01:00

Answer:

B) The longer leg is √3 times as long as the shorter leg.

C) The hypotenuse is twice as long as the shorter leg.

Step-by-step explanation:

Consider the provided information.

The provided triangle is 30- 60-90 degree triangle.

We use the common ratio of 30- 60-90 degree triangle

Common ratio is [tex]1:\sqrt{3} :2[/tex]

The larges side length is always opposite the 90° and the smallest side length is always opposite the 30°.

Let the smallest length is x.

30 : 60 : 90

Short leg : long leg : hypotenuse

x : [tex]x\sqrt{3}[/tex] : 2x

The hypotenuse is 2 times of the shorter leg.

longer leg is square root (3) times the shorter leg.

Hence, the correct options are:

B) The longer leg is √3 times as long as the shorter leg.

C) The hypotenuse is twice as long as the shorter leg.