Question

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

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle X\), the adjacent side to \(\angle X\) is \(XZ\) and the hypotenuse is \(XY\).

Step2: Identify the lengths

We are given that \(XZ = 16\) and \(XY=34\).

Step3: Calculate \(\cos(X)\)

Using the formula \(\cos(X)=\frac{XZ}{XY}\), substitute the values: \(\cos(X)=\frac{16}{34}\). Simplify the fraction by dividing both the numerator and the denominator by 2. So, \(\frac{16\div2}{34\div2}=\frac{8}{17}\).

Answer:

\(\frac{8}{17}\)