Question

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

Explanation:

Step1: Recall tangent formula

$\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$ for right - triangle.

Step2: Identify sides for $\angle Y$

For $\angle Y$, opposite side to $\angle Y$ is $XZ$ and adjacent is $YZ$. In a 30 - 60 - 90 triangle with hypotenuse $XY = 4$, $XZ=\frac{1}{2}XY = 2$ and $YZ = 2\sqrt{3}$.

Step3: Calculate $\tan(Y)$

$\tan(Y)=\frac{XZ}{YZ}=\frac{2}{2\sqrt{3}}=\frac{\sqrt{3}}{3}$

Answer:

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