Question

Find tan , where is the angle shown. Give an exact value, not a decimal approximation. tane = II 13 12

Answer 1

We will find the value of

`\tan \theta`

where θ is the angle shown. We remember that in a right triangle,

`\begin{gathered} \tan \theta=(op)/(ad) \\ \text{where op is the opposite side to }\theta,\text{ and ad is the adjacent side to }\theta \end{gathered}`

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:

`\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}`

This means that the value of ad is 5.

With this is mind, we will find the value of tangent, and we get:

`\tan \theta=(12)/(5)`

Thus, the value of tan θ is 12/5.