Question

find the exact value of \\(\cos p\\) in simplest radical form.
answer attempt 1 out of 2
\\(\cos p =\\)

Explanation:

Step1: Recall cosine definition for right triangles

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

Step2: Identify sides for angle $P$

Adjacent side to $P$: $\sqrt{27}$, Hypotenuse: $14$

Step3: Simplify the radical

$\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$

Step4: Substitute and simplify $\cos P$

$\cos P = \frac{3\sqrt{3}}{14}$

Answer:

$\frac{3\sqrt{3}}{14}$