Question

find the exact value of cos f in simplest radical form.

Explanation:

Step1: Recall cosine definition in right triangle

In a right triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\) for an angle \(\theta\). For \(\angle F\), the adjacent side to \(\angle F\) is \(FG = \sqrt{32}\) and the hypotenuse is \(FH=7\). But first, simplify \(\sqrt{32}\).
\(\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}\)

Step2: Apply cosine formula

Now, \(\cos F=\frac{\text{adjacent to }F}{\text{hypotenuse}}=\frac{FG}{FH}\)
Substitute \(FG = 4\sqrt{2}\) and \(FH = 7\) into the formula.
\(\cos F=\frac{4\sqrt{2}}{7}\)

Answer:

\(\frac{4\sqrt{2}}{7}\)