Question

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

Explanation:

Step1: Find the length of FG

In right triangle \( FGH \), by the Pythagorean theorem \( FH^2 = FG^2 + GH^2 \). We know \( FH = 20 \) and \( GH = 16 \), so \( FG=\sqrt{FH^{2}-GH^{2}}=\sqrt{20^{2}-16^{2}}=\sqrt{400 - 256}=\sqrt{144} = 12 \).

Step2: Calculate \( \cos(F) \)

In a right triangle, \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). For \( \angle F \), the adjacent side is \( FG = 12 \) and the hypotenuse is \( FH = 20 \). So \( \cos(F)=\frac{FG}{FH}=\frac{12}{20}=\frac{3}{5} \).

Answer:

\(\frac{3}{5}\)