Question

what is cot(∠a)? reduce fractional answers to lowest terms. right triangle with right angle at c, ac = 6, bc = 8, ab = 10, vertices a, b, c

Explanation:

Step1: Recall cotangent definition

In a right triangle, $\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}$ to $\theta$. For $\angle A$, adjacent side is $AC = 6$, opposite side is $BC = 8$.

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

$\cot(\angle A) = \frac{AC}{BC} = \frac{6}{8}$

Step3: Simplify the fraction

Simplify $\frac{6}{8}$ by dividing numerator and denominator by 2: $\frac{6\div2}{8\div2} = \frac{3}{4}$

Answer:

$\frac{3}{4}$