Question

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

Explanation:

Step1: Recall cosine - definition in right - triangle

In right - triangle $\triangle WXY$ with right - angle at $W$, $\cos(Y)=\frac{adjacent}{hypotenuse}$. The side adjacent to $\angle Y$ is $WY$ and the hypotenuse is $XY$. First, find the length of the hypotenuse $XY$ using the Pythagorean theorem.

Step2: Apply Pythagorean theorem

In right - triangle $\triangle WXY$, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 16$ (length of $WY$) and $b = 30$ (length of $WX$). So, $XY=\sqrt{16^{2}+30^{2}}=\sqrt{256 + 900}=\sqrt{1156}=34$.

Step3: Calculate cosine of $\angle Y$

Since $\cos(Y)=\frac{WY}{XY}$, and $WY = 16$, $XY = 34$, then $\cos(Y)=\frac{16}{34}=\frac{8}{17}$.

Answer:

$\frac{8}{17}$