Question

question find the exact value of tan g in simplest radical form. answer attempt 1 out of 2

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle G$ in right - triangle $GHI$ with right - angle at $H$, the side opposite to $\angle G$ is $HI = \sqrt{45}$, and the side adjacent to $\angle G$ is $GH=22$.

Step2: Simplify the radical

We know that $\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}$. So, $\tan G=\frac{\sqrt{45}}{22}=\frac{3\sqrt{5}}{22}$.

Answer:

$\frac{3\sqrt{5}}{22}$