Question

find the tangent of \\( \angle b \\).
simplify your answer and write it as a proper fraction, improper fraction, or whole number.
\\( \tan ( b ) = \\)

Explanation:

Step1: Recall the tangent formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle B\), the side opposite to \(\angle B\) is \(DC = 12\) and the side adjacent to \(\angle B\) is \(BC=5\).

Step2: Calculate \(\tan(B)\)

Using the formula \(\tan(B)=\frac{DC}{BC}\), substituting \(DC = 12\) and \(BC = 5\), we get \(\tan(B)=\frac{12}{5}\).

Answer:

\(\frac{12}{5}\)