so hmmm notice the picture below
thus
[tex]\bf cos(\theta)=\cfrac{8}{17}\cfrac{\leftarrow adjacent=a}{\leftarrow hypotenuse=c}
\\\\\\
\textit{now, using the pythagorean theorem, let's see what "b" is}
\\\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\implies \pm\sqrt{17^2-8^2}=b
\\\\\\
\pm \sqrt{225}=b\implies \pm 15=b[/tex]
now, which is it? +15 or -15? well, the "y" or sine, is positive on the 1st quadrant, and the angle θ, is on the 1st quadrant, thus is +15
[tex]\bf sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad \qquad
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}
\\ \quad \\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}\\\\
-----------------------------\\\\
sin(\theta)=\cfrac{15}{17}\qquad \qquad tan(\theta)=\cfrac{15}{8}[/tex]
