Question

given right triangle xyz, what is the value of tan(y)? o 1/2 o √3/3 o √3/2 o 2√3/3

Explanation:

Step1: Recall tangent formula

$\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$ in a right - triangle. In right - triangle $XYZ$ with $\angle Y = 30^{\circ}$, if we assume the side opposite to $\angle Y$ is $x$ and the side adjacent to $\angle Y$ is $\sqrt{3}x$.

Step2: Calculate $\tan(Y)$

$\tan(Y)=\tan(30^{\circ})=\frac{x}{\sqrt{3}x}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$

Answer:

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