Question

find the tangent of ∠e.

(there is a right triangle edc with right angle at d. ed = 36, dc = 77, ec = 85)

simplify your answer and write it as a proper fraction, improper fraction, or whole number.

tan(e) =
(there are buttons for fraction and square root below the answer box)

Explanation:

Step1: Recall tangent definition

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

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

For \(\angle E\) in right \(\triangle EDC\) (right - angled at \(D\)), the side opposite to \(\angle E\) is \(DC = 77\) and the side adjacent to \(\angle E\) is \(ED=36\).

Step3: Calculate \(\tan(E)\)

Using the tangent formula \(\tan(E)=\frac{\text{opposite to }E}{\text{adjacent to }E}=\frac{DC}{ED}\).
Substituting \(DC = 77\) and \(ED = 36\), we get \(\tan(E)=\frac{77}{36}\).

Answer:

\(\frac{77}{36}\)