Question

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in \\( \triangle efg \\), the measure of \\( \angle g = 90 ^ { \circ }, fe = 89, gf = 80 \\), and \\( eg = 39 \\). what ratio represents the tangent of \\( \angle e \\)?
answer attempt 1 out of 2
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Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, for an angle \(\theta\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Identify the sides relative to \(\angle E\)

For \(\angle E\) in right - triangle \(EFG\) with \(\angle G = 90^{\circ}\), the side opposite to \(\angle E\) is \(GF\) and the side adjacent to \(\angle E\) is \(EG\).

Step3: Calculate the tangent ratio

We know that \(GF = 80\) and \(EG=39\). So, \(\tan E=\frac{GF}{EG}\).

Answer:

\(\frac{80}{39}\)