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 definition

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

Step2: Identify sides for $\angle C$

In right triangle $BCD$ (right - angled at $B$), for $\angle C$:

• Opposite side to $\angle C$ is $BD = 24$
• Adjacent side to $\angle C$ is $BC=10$

Step3: Calculate $\tan(C)$

Using the tangent formula $\tan(C)=\frac{\text{opposite to }C}{\text{adjacent to }C}=\frac{BD}{BC}=\frac{24}{10}$
Simplify $\frac{24}{10}$ by dividing numerator and denominator by their greatest common divisor, which is 2. So $\frac{24\div2}{10\div2}=\frac{12}{5}$

Answer:

$\frac{12}{5}$