Question

find the exact value of \\( \cos v \\) in simplest radical form.

Explanation:

Step1: Recall the cosine formula

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

Step2: Identify the lengths

We are given that \(VW = \sqrt{48}\) and \(VX=8\).

Step3: Calculate \(\cos V\)

\(\cos V=\frac{VW}{VX}=\frac{\sqrt{48}}{8}\). Simplify \(\sqrt{48}=\sqrt{16\times3} = 4\sqrt{3}\). Then \(\cos V=\frac{4\sqrt{3}}{8}\).

Step4: Simplify the fraction

Cancel out the common factor of 4 in the numerator and denominator. \(\frac{4\sqrt{3}}{8}=\frac{\sqrt{3}}{2}\)

Answer:

\(\frac{\sqrt{3}}{2}\)