Question

find de.
write your answer as an integer or as a decimal rounded to the nearest tenth.
de =

Explanation:

Step1: Identify adjacent side to $\angle E$

We know $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, where $\theta=23^\circ$, adjacent side $CE=\sqrt{74}$, hypotenuse is $DE$.

Step2: Rearrange to solve for $DE$

$$DE = \frac{\sqrt{74}}{\cos(23^\circ)}$$

Step3: Calculate value

First, $\sqrt{74} \approx 8.602$, $\cos(23^\circ)\approx0.9205$. Then $\frac{8.602}{0.9205}\approx9.3$.

Answer:

$9.3$