Question

find the tangent of ∠y. simplify your answer and write it as a proper number. tan(y) =

Explanation:

Step1: Recall tangent - ratio formula

The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle Y$, the side opposite to $\angle Y$ is $WX = 56$, and the side adjacent to $\angle Y$ is $XY$.

Step2: Find the length of $XY$ using Pythagorean theorem

In right - triangle $WXY$, by the Pythagorean theorem $WY^{2}=WX^{2}+XY^{2}$. Given $WY = 65$ and $WX = 56$, we have $XY=\sqrt{WY^{2}-WX^{2}}=\sqrt{65^{2}-56^{2}}=\sqrt{(65 + 56)(65 - 56)}=\sqrt{121\times9}=\sqrt{1089}=33$.

Step3: Calculate $\tan(Y)$

$\tan(Y)=\frac{WX}{XY}$. Substituting $WX = 56$ and $XY = 33$, we get $\tan(Y)=\frac{56}{33}$.

Answer:

$\frac{56}{33}$