To answer this question we need to remember the definition of the trigonometric functions:
[tex]\sin \theta=\frac{\text{opp}}{\text{hyp}}[/tex][tex]\cos \theta=\frac{\text{adj}}{\text{hyp}}[/tex][tex]\tan \theta=\frac{\text{opp}}{\text{adj}}[/tex]
where opp denotes the opposite leg of the angle, adj the adjacent leg of the angle and hyp the hypotenuse.
Now, in this triangle we notice that for angle B the opposite leg is 15, the adjacent leg is 8 and the hypotenuse is 17. Plugging this values into the definitions above we have that:
[tex]\tan B=\frac{15}{8}[/tex][tex]\sin B=\frac{15}{17}[/tex][tex]\cos B=\frac{8}{17}[/tex]
