express \\(\\cos p\\) as a fraction in simplest terms.

Explanation:

Step1: Recall cosine definition

For an acute angle in a right triangle, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle P$

Adjacent to $\angle P$: $PO = 15$, Hypotenuse: $PN = 39$

Step3: Substitute and simplify fraction

$\cos P = \frac{15}{39} = \frac{15\div3}{39\div3} = \frac{5}{13}$

Answer:

$\frac{5}{13}$