Question

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

Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle D\), the side opposite to \(\angle D\) is \(CE = 48\), and the side adjacent to \(\angle D\) is \(CD=20\).

Step2: Calculate \(\tan(D)\)

Using the formula \(\tan(D)=\frac{CE}{CD}\), substitute \(CE = 48\) and \(CD = 20\). So, \(\tan(D)=\frac{48}{20}\). Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. The GCD of 48 and 20 is 4. \(\frac{48\div4}{20\div4}=\frac{12}{5}\).

Answer:

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