Question

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

Explanation:

Step1: Identify known values

We know $\angle CDE = 27^\circ$, $CE=4$, and $CE = DE$'s opposite side for $\angle D$, $\cos(\angle CDE) = \frac{DE}{CD}$, $\sin(\angle CDE)=\frac{CE}{CD}$.

Step2: Solve for CD

$$CD = \frac{CE}{\sin(27^\circ)}$$
Substitute $CE=4$, $\sin(27^\circ)\approx0.4540$:
$$CD \approx \frac{4}{0.4540} \approx 8.8$$

Answer:

$8.8$