Question

use the following triangle to find tan θ. note: enter the exact, fully simplified and rationalized answer. tan θ =

Explanation:

Step1: Recall tangent formula

The formula for $\tan\theta$ in a right - triangle is $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify opposite and adjacent sides

For angle $\theta$, the opposite side has length $7$ and the adjacent side has length $\sqrt{74}$.
So, $\tan\theta = \frac{7}{\sqrt{74}}$.

Step3: Rationalize the denominator

Multiply the numerator and denominator by $\sqrt{74}$: $\tan\theta=\frac{7\sqrt{74}}{74}$.

Answer:

$\frac{7\sqrt{74}}{74}$