Question

solving problems with right triangles
in this activity, you will apply your understanding of right triangles to solve problems.
question 1
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: Recall the 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 \(\theta\) is \(XY\).

Step2: Apply the sine formula

We know that \(\sin30^{\circ}=\frac{XY}{XZ}\). Since \(\sin30^{\circ}=\frac{1}{2}\) and \(XZ = 12\), substituting the values into the formula gives \(\frac{1}{2}=\frac{XY}{12}\).

Step3: Solve for \(XY\)

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

Answer:

\(6\)