Question

find the exact value of tan r in simplest radical form.

Explanation:

Step1: Recall tangent - ratio formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle R$ in right - triangle $RST$, the side opposite $\angle R$ is $ST$ and the side adjacent to $\angle R$ is $RS$.

Step2: Identify opposite and adjacent sides

We are given that $RS = 8$ and $ST=\sqrt{21}$.

Step3: Calculate $\tan R$

Using the formula $\tan R=\frac{ST}{RS}$, we substitute the values: $\tan R=\frac{\sqrt{21}}{8}$.

Answer:

$\frac{\sqrt{21}}{8}$