Question

given right triangle xyz, what is the value of tan(y)?

Explanation:

Step1: Recall tangent formula

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

Step2: Identify side lengths

Let's assume the length of the side opposite to angle $Y$ (side $XZ$) is $x$ and the length of the side adjacent to angle $Y$ (side $XY$) is $y$. Then $\tan(Y)=\frac{XZ}{XY}$.

Step3: Calculate the ratio

If we assume from the right - triangle properties (assuming we know the side lengths from the figure, if for example, $XZ = 1$ and $XY=\sqrt{3}$), then $\tan(Y)=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$.

Answer:

$\frac{\sqrt{3}}{3}$