We can break the triangle into smaller and bigger triangles.
For the smaller triangle, we can get the length of the base using the tan ratio:
[tex]\tan\theta=\frac{opp}{adj}[/tex]
From the image, we have:
[tex]\begin{gathered} \theta=68\degree \\ opp=80 \\ adj=? \end{gathered}[/tex]
Therefore, we have:
[tex]\begin{gathered} \tan68=\frac{80}{adj} \\ adj=\frac{80}{\tan68} \\ adj=32.32 \end{gathered}[/tex]
For the bigger triangle, the base can be calculated using the same tan ratio but with the following parameters:
[tex]\theta=23\degree[/tex]
Therefore, we have:
[tex]\begin{gathered} \tan23=\frac{80}{adj} \\ adj=\frac{80}{\tan23} \\ adj=188.47 \end{gathered}[/tex]
From the image, we have that:
[tex]32.32+x=188.47[/tex]
Therefore, we can solve for x as shown below:
[tex]\begin{gathered} x=188.47-32.32 \\ x=156.15 \end{gathered}[/tex]
The value of x is 156.15 units.
