Given the triangle ABC, you know that:
[tex]\begin{gathered} AB=10 \\ AC=6 \\ BC=8 \end{gathered}[/tex]You can identify that the small square in the vertex C of the triangle is a Right Angle (an angle that measures 90 degrees). Therefore, you have to find the tangent of the other two angles:
[tex]\begin{gathered} \angle A \\ \angle B \end{gathered}[/tex]By definition:
[tex]tan\theta=\frac{opposite}{adjacent}[/tex]Then:
- For angle A, you can identify that:
[tex]\begin{gathered} \theta=A \\ opposite=BC=8 \\ adjacent=AC=6 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} tan(A)=\frac{8}{6} \\ \\ tan(A)=\frac{4}{3} \end{gathered}[/tex]- For angle B:
[tex]\begin{gathered} \theta=B \\ opposite=AC=6 \\ adjacent=BC=8 \end{gathered}[/tex]Therefore, you get:
[tex]\begin{gathered} tan(B)=\frac{6}{8} \\ \\ tan(B)=\frac{3}{4} \end{gathered}[/tex]Hence, the answer is:
[tex]\begin{gathered} tan(A)=\frac{4}{3} \\ \\ tan(B)=\frac{3}{4} \end{gathered}[/tex]