Question

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

Explanation:

Step1: Recall tangent formula

In a right - triangle, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle C$, the opposite side to $\angle C$ is $BD$ and the adjacent side is $CD$.

Step2: Identify side lengths

We are given that $BD = 24$ (opposite to $\angle C$) and $CD=10$ (adjacent to $\angle C$).

Step3: Calculate tangent

$\tan(C)=\frac{BD}{CD}=\frac{24}{10}=\frac{12}{5}$

Answer:

$\frac{12}{5}$