Question

find the cotangent of ∠d.
triangle with vertices e, f, d; right angle at e; ef = 3, ed = √7, fd = 4
write your answer in simplified, rationalized form. do not round.
cot(d) =

Explanation:

Step1: Recall cotangent definition

In a right triangle, \(\cot(\theta)=\frac{\text{adjacent}}{\text{opposite}}\) to \(\theta\).

Step2: Identify sides for \(\angle D\)

For \(\angle D\), adjacent side is \(DE = \sqrt{7}\), opposite side is \(EF = 3\).

Step3: Calculate \(\cot(D)\)

\(\cot(D)=\frac{DE}{EF}=\frac{\sqrt{7}}{3}\)

Answer:

\(\frac{\sqrt{7}}{3}\)