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

Explanation:

Step1: Identify trig - ratio

In right - triangle $CDE$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 46^{\circ}$ and the hypotenuse $CE$ is what we want to find, and the adjacent side to $\angle E$ is $DE=\sqrt{37}$.

Step2: Apply cosine formula

We know that $\cos E=\cos46^{\circ}=\frac{DE}{CE}$. So, $CE=\frac{DE}{\cos46^{\circ}}$. Since $DE = \sqrt{37}\approx6.083$, and $\cos46^{\circ}\approx0.695$.

Step3: Calculate $CE$

$CE=\frac{\sqrt{37}}{\cos46^{\circ}}\approx\frac{6.083}{0.695}\approx8.8$.

Answer:

$8.8$