Question

the top of a waterslide is 8 meters above the ground, and its base is 12 meters from the ladder.
which equation will calculate the angle of the slide with the ground?
$\bigcirc x = \tanleft(\frac{12}{8}
ight)$
$\bigcirc \tan(x) = \frac{12}{8}$
$\bigcirc \tan(x) = \frac{8}{12}$
$\bigcirc x = \tanleft(\frac{8}{12}
ight)$

Explanation:

Step1: Identify right triangle sides

For angle $x$, opposite side $=8$, adjacent side $=12$.

Step2: Recall tangent definition

$\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}$

Step3: Substitute values into formula

$\tan(x) = \frac{8}{12}$

Answer:

$\boldsymbol{\tan(x) = \frac{8}{12}}$ (corresponding to the third option)