Question

find the tangent of ∠h. write your answer in simplified, rationalized form. do not round. tan(h) =

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$ for an acute angle $\theta$. For $\angle H$ in right - triangle $GHI$, the side opposite $\angle H$ is $GI$ and the side adjacent to $\angle H$ is $HI$.

Step2: Identify the lengths of the opposite and adjacent sides

We are given that $GI = \sqrt{73}$ and $HI=\sqrt{21}$.

Step3: Calculate the tangent of $\angle H$

$\tan(H)=\frac{GI}{HI}=\frac{\sqrt{73}}{\sqrt{21}}$.

Step4: Rationalize the denominator

Multiply the numerator and denominator by $\sqrt{21}$: $\tan(H)=\frac{\sqrt{73}\times\sqrt{21}}{\sqrt{21}\times\sqrt{21}}=\frac{\sqrt{73\times21}}{21}=\frac{\sqrt{1533}}{21}$.

Answer:

$\frac{\sqrt{1533}}{21}$