Question

given right triangle gyk, what is the value of tan(g)?
o $\frac{1}{2}$
o $\frac{sqrt{3}}{2}$
o $\frac{2sqrt{3}}{3}$
o $sqrt{3}$

Explanation:

Step1: Recall tangent formula

The formula for the tangent of an angle in a right - triangle is $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. In right - triangle $GYK$, for angle $G$, the opposite side to angle $G$ is $YK$ and the adjacent side is $GK$.

Step2: Use trigonometric relationships

We know that in a $30 - 60-90$ triangle, if the side adjacent to the $60^{\circ}$ angle ($GK = 27$) and the hypotenuse $GY = 30$. We can also use the fact that $\tan(G)=\tan(60^{\circ})$. The value of $\tan(60^{\circ})=\sqrt{3}$.

Answer:

$\sqrt{3}$