find the cosine of ∠e. simplify your answer and write it as a proper fraction, improper fraction, or whole…

Explanation:

Step1: Recall cosine - ratio definition

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle E$ in right - triangle $DCE$, the side adjacent to $\angle E$ is $CE$ and the hypotenuse is $DE$.

Step2: Identify side lengths

We know that $DE = 73$ and $CE$ can be found using the Pythagorean theorem. First, by the Pythagorean theorem $CE=\sqrt{DE^{2}-DC^{2}}$. Given $DC = 55$ and $DE = 73$, then $CE=\sqrt{73^{2}-55^{2}}=\sqrt{(73 + 55)(73 - 55)}=\sqrt{128\times18}=\sqrt{2304}=48$.

Step3: Calculate $\cos(E)$

Using the cosine - ratio formula $\cos(E)=\frac{CE}{DE}$. Substituting $CE = 48$ and $DE = 73$, we get $\cos(E)=\frac{48}{73}$.

Answer:

$\frac{48}{73}$