Question

use right triangle xyz to complete the following parts.
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= \\) units

Explanation:

Step1: Use sine function

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 30^{\circ}$, the hypotenuse $XZ = 12$, and the side opposite to the $30^{\circ}$ angle is $XY$.
So, $\sin30^{\circ}=\frac{XY}{XZ}$.

Step2: Substitute the values

Since $\sin30^{\circ}=\frac{1}{2}$ and $XZ = 12$, we have $\frac{1}{2}=\frac{XY}{12}$.

Step3: Solve for $XY$

Cross - multiply: $XY=\frac{1\times12}{2}$.

Answer:

$6$