We are given one angle and the adjacent side of a right triangle and we are asked to find the opposite side using a trigonometric function. The trigonometric function that relates the opposite and adjacent sides is "tangent" since it is definine as follows;
[tex]\tan \theta=\frac{\text{opposite}}{\text{adjacent}}[/tex]
In this case we have the following values:
[tex]\begin{gathered} \text{Opposite}=x \\ \text{Adjacent}=12 \\ \theta=25^0 \end{gathered}[/tex]
Replacing the values we get:
[tex]\tan 25=\frac{x}{12}[/tex]
Now we solve for "x" by multiplying by 12 on both sides:
[tex]12\tan 25=x[/tex]
Solving the operations we got:
[tex]5.59=x[/tex]
Therefore, the value of the missing sie is approximately 5.6
