Question

what is cot(∠a)? reduce fractional answers to lowest terms. triangle with right angle at c, ac=12, cb=5, ab=13

Explanation:

Step1: Recall cotangent definition

In a right triangle, $\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}$ to angle $\theta$. For $\angle A$, adjacent side is $AC$ and opposite side is $BC$.
Given $AC = 12$, $BC = 5$.

Step2: Calculate $\cot(\angle A)$

Using the definition, $\cot(\angle A) = \frac{AC}{BC} = \frac{12}{5}$.

Answer:

$\frac{12}{5}$