Question

express tan g as a fraction in simplest terms.
answer attempt 1 out of 2
tan g =

Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle G\), the side opposite to \(\angle G\) is \(EF = 32\) and the side adjacent to \(\angle G\) is \(GF=24\).

Step2: Calculate \(\tan G\)

\(\tan G=\frac{EF}{GF}\)
Substitute \(EF = 32\) and \(GF = 24\) into the formula: \(\tan G=\frac{32}{24}\)
Simplify the fraction \(\frac{32}{24}\) by dividing both the numerator and the denominator by their greatest common divisor. The GCD of 32 and 24 is 8.
\(\frac{32\div8}{24\div8}=\frac{4}{3}\)

Answer:

\(\frac{4}{3}\)