Question

using \\( \angle c f d \\) as the reference angle, what is the tang
\\( \frac { 8 } { 15 } \\)
\\( \frac { 8 } { 17 } \\)
\\( \frac { 15 } { 17 } \\)
\\( \frac { 15 } { 8 } \\)

Explanation:

Step1: Recall the tangent formula

The tangent of an angle in a right - triangle is defined as \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle CFD \), the side opposite to \( \angle CFD \) is \( CD = 8 \), and the side adjacent to \( \angle CFD \) is \( DF=15 \).

Step2: Calculate the tangent value

Using the formula \( \tan\angle CFD=\frac{CD}{DF} \), substituting \( CD = 8 \) and \( DF = 15 \), we get \( \tan\angle CFD=\frac{8}{15} \).

Answer:

\(\frac{8}{15}\)