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express tan f as a fraction in simplest
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tan f =
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Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For angle $F$, the side opposite to angle $F$ is $GH = 6$, and the side adjacent to angle $F$ is $FG=10$.

Step2: Calculate $\tan F$

$\tan F=\frac{GH}{FG}=\frac{6}{10}$.

Step3: Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor. The GCD of 6 and 10 is 2. So, $\frac{6\div2}{10\div2}=\frac{3}{5}$.

Answer:

$\frac{3}{5}$