Question

part a
question
what is the length of \\(\overline{xy}\\) in \\(\triangle xyz\\)?
type the correct answer in the box. use numerals instead of words.
\\(xy = \\) \\(\quad\\) units

Explanation:

Step1: Identify triangle type

$\triangle XYZ$ is a right - triangle with $\angle Y = 90^{\circ}$, $\angle Z=30^{\circ}$, and hypotenuse $XZ = 12$ units.

Step2: Use 30 - 60 - 90 triangle property

In a 30 - 60 - 90 right - triangle, the side opposite the $30^{\circ}$ angle (which is $XY$ here, since $\angle Z = 30^{\circ}$ and $XY$ is opposite to $\angle Z$) is half of the hypotenuse. So, $XY=\frac{1}{2}\times XZ$.

Step3: Calculate $XY$

Substitute $XZ = 12$ into the formula: $XY=\frac{1}{2}\times12 = 6$.

Answer:

6