Question

find the cosine of ∠w. simplify your answer and write it as a proper fraction number. cos (w) =

Explanation:

Step1: Recall cosine - ratio definition

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle W$, the adjacent side to $\angle W$ is $WX$ and the hypotenuse is $WY$.

Step2: Identify side lengths

We know that $WX$ needs to be found using the Pythagorean theorem. Let $WX = a$, $XY = 4$, and $WY = 5$. By the Pythagorean theorem $a=\sqrt{WY^{2}-XY^{2}}=\sqrt{25 - 16}=\sqrt{9}=3$. The adjacent side to $\angle W$ is $3$ and the hypotenuse is $5$.

Step3: Calculate cosine value

$\cos(W)=\frac{\text{adjacent to }\angle W}{\text{hypotenuse}}=\frac{3}{5}$

Answer:

$\frac{3}{5}$