We will find the value of
[tex]\tan \theta[/tex]
where θ is the angle shown. We remember that in a right triangle,
[tex]\begin{gathered} \tan \theta=\frac{op}{ad} \\ \text{where op is the opposite side to }\theta,\text{ and ad is the adjacent side to }\theta \end{gathered}[/tex]
In this exercise, we have the value of the opposite side, but we need the length of the adjacent side. We will use the Pythagorean Theorem for finding it:
[tex]\begin{gathered} h^2=op^2+ad^2 \\ 13^2=12^2+ad^2 \\ 169=144+ad^2 \\ 169-144=ad^2 \\ 25=ad^2 \\ \sqrt[]{25}=ad \\ 5=ad \end{gathered}[/tex]
This means that the value of ad is 5.
With this is mind, we will find the value of tangent, and we get:
[tex]\tan \theta=\frac{12}{5}[/tex]
Thus, the value of tan θ is 12/5.
