Flashcard 14 - 11th Grade Mathematics: Geometry Flashcard Set for the SBAC

\[\dfrac{12}{5}\]

\[\cos(\theta) = \dfrac{\text{adjacent}}{\text{hypotenuse}}\]

So, the adjacent side is \(5\) and the hypotenuse is \(13\) units.

Use the Pythagorean theorem to find the opposite side:

\[\text{opp}^2 + 5^2 = 13^2\] \[\text{opp}^2 + 25 = 169\] \[\text{opp}^2 = 144\] \[\text{opp} = 12\]

Now, find \(\tan(\theta) = \dfrac{\text{opposite}}{\text{adjacent}} = \dfrac{12}{5}\)