Question

the length of segment ab is 9 mm. which statements regarding triangle abc are correct? check all that apply. ab is the shortest segment in △abc. bc = 18mm. ac = 2ab. ac = 9√3. bc is the longest segment in △abc.

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratio

In a 30 - 60 - 90 triangle, if the side opposite 30° is $a$, the side opposite 60° is $a\sqrt{3}$ and the hypotenuse is $2a$. Here $AB$ (opposite 30°) is 9 mm.

Step2: Calculate other sides

$BC = 9\sqrt{3}$ mm and $AC=18$ mm.

Answer:

AC = 2AB, BC = 9$\sqrt{3}$, AB is the shortest segment in △ABC