given right triangle gyk, what is the value of tan(g)?\no $\frac{1}{2}$\no $\frac{sqrt{3}}{2}$\no…

Explanation:

Step1: Recall tangent - ratio formula

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

Step2: Identify the sides for $\angle G$

We know that in right - triangle $GYK$, $\angle G = 60^{\circ}$ and $GK = 27$. In a 30 - 60 - 90 right - triangle, if the shorter leg (adjacent to the $60^{\circ}$ angle) is $a$, the longer leg (opposite the $60^{\circ}$ angle) is $a\sqrt{3}$. Here $a = GK=27$, and $YK = 27\sqrt{3}$.

Step3: Calculate $\tan(G)$

Using the formula $\tan(G)=\frac{YK}{GK}$, substituting $YK = 27\sqrt{3}$ and $GK = 27$, we get $\tan(G)=\frac{27\sqrt{3}}{27}=\sqrt{3}$.

Answer:

$\sqrt{3}$