We are given a right triangle and we have to find the length of one of its sides. It will be useful to remember the definition of the tangent of an angle inside a right triangle. For an angle α<90° in a right triangle we have:
[tex]\tan \alpha=\frac{\text{opposite side}}{\text{adjacent side}}[/tex]
If α is the 26° angle in the image then its opposite side is 11 and its adjacent side is x. Then we get:
[tex]\tan 26^{\circ}=\frac{11}{x}[/tex]
We can multiply both sides of this equation by x:
[tex]\begin{gathered} \tan 26^{\circ}\cdot x=\frac{11}{x}\cdot x \\ \tan 26^{\circ}\cdot x=11 \end{gathered}[/tex]
And we divide both sides by tan(26°):
[tex]\begin{gathered} \frac{\tan 26^{\circ}\cdot x}{\tan 26^{\circ}}=\frac{11}{\tan 26^{\circ}} \\ x=\frac{11}{\tan26^{\circ}}=22.6 \end{gathered}[/tex]
Then the answer is 22.6.
