In $\triangle{XYZ}$, $\angle{Z}=90^{\circ}$, $\cos{Y}=\frac{7}{25}$, and $XY=25$.  What is $\tan{X}$?
I know that $\cos{Y}=\frac{7}{25}$ means that the adjacent side to angle $Y$ is $7$ units long and the hypotenuse is $25$ units long. I can use the Pythagorean theorem to find the opposite side to angle $Y$, which is also the adjacent side to angle $X$. Let me call that side $a$. Then $a^2+7^2=25^2$. Simplifying, I get $a^2=576$, so $a=24$. Now I have all the sides of the right triangle, so I can find $\tan{X}$. I know that $\tan{X}=\frac{\text{opposite}}{\text{adjacent}}$, so $\tan{X}=\frac{7}{24}$. That's my answer. 