### Instruction: In $\triangle{XYZ}$, $\angle{Z}=90^{\circ}$, $\cos{Y}=\frac{7}{25}$, and $XY=25$.  What is $\tan{X}$?### Response: 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.