Answer:
[tex]tan(B)=\frac{8}{6}[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle ABC of the figure
1) The tangent of angle B is equal to divide the opposite side angle B to the adjacent side to angle B
so
[tex]tan(B)=\frac{AC}{BC}[/tex]
substitute the given values
[tex]tan(B)=\frac{8}{6}[/tex]
2) The sine of angle B is equal to divide the opposite side angle B to the hypotenuse
[tex]sin(B)=\frac{AC}{AB}[/tex]
substitute the given values
[tex]sin(B)=\frac{8}{10}[/tex]
3) The cosine of angle B is equal to divide the adjacent side angle B to the hypotenuse
[tex]cos(B)=\frac{BC}{AB}[/tex]
substitute the given values
[tex]cos(B)=\frac{6}{10}[/tex]
therefore
The answer is
[tex]tan(B)=\frac{8}{6}[/tex]
