Question

find the tangent of ∠e. simplify your answer and write it as a proper fraction, improper fraction, or whole number. tan (e) =

Explanation:

Step1: Find side CD length

Use Pythagorean theorem:
$$CD = \sqrt{CE^2 - DE^2} = \sqrt{89^2 - 39^2} = \sqrt{7921 - 1521} = \sqrt{6400} = 80$$

Step2: Define tangent for ∠E

Recall $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$:
$$\tan(E) = \frac{CD}{DE}$$

Step3: Substitute values and simplify

$$\tan(E) = \frac{80}{39}$$

Answer:

$\frac{80}{39}$