Question

find the tangent of \\( \angle y \\).
simplify your answer and write it as a proper fraction, improper fraction, or whole number.
\\( \tan ( y ) = \\)

Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle Y\), the side opposite to \(\angle Y\) is \(XZ = 24\) and the side adjacent to \(\angle Y\) is \(XY=10\).

Step2: Calculate \(\tan(Y)\)

Using the formula \(\tan(Y)=\frac{\text{opposite}}{\text{adjacent}}\), we substitute the values: \(\tan(Y)=\frac{XZ}{XY}\).
Since \(XZ = 24\) and \(XY = 10\), then \(\tan(Y)=\frac{24}{10}\).
Simplify the fraction \(\frac{24}{10}=\frac{12}{5}\) (divide numerator and denominator by 2).

Answer:

\(\frac{12}{5}\)