Question

find the cosine of ∠c. write your answer in simplified, rationalized form. do not round. cos(c) =

Explanation:

Step1: Recall cosine - ratio in right - triangle

In a right - triangle, $\cos(C)=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Identify adjacent and hypotenuse sides

The side adjacent to $\angle C$ is $CD$ and the hypotenuse is $BC$. Given $CD = \sqrt{5}$ and $BC=2\sqrt{5}$.

Step3: Calculate the cosine value

$\cos(C)=\frac{CD}{BC}=\frac{\sqrt{5}}{2\sqrt{5}}$.

Step4: Simplify the fraction

$\frac{\sqrt{5}}{2\sqrt{5}}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$