Question

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

Explanation:

Step1: Identify right triangle sides

$\triangle WXY$ is right-angled at $X$. For $\angle Y$, adjacent side $XY=8$, hypotenuse $WY=17$.

Step2: Calculate opposite side $XW$

Use Pythagoras: $XW=\sqrt{WY^2 - XY^2}=\sqrt{17^2 - 8^2}=\sqrt{289-64}=\sqrt{225}=15$.

Step3: Compute $\tan(Y)$

$\tan(Y)=\frac{\text{opposite}}{\text{adjacent}}=\frac{XW}{XY}=\frac{15}{8}$.

Answer:

$\frac{15}{8}$