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In $\triangle X Y Z, \angle Z=90^{\circ}, \cos Y=\frac{7}{25}$, and $X Y=25 .$ What is $\tan X ?$
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Since $\angle Z$ is the right angle, our triangle is shown below: (figure) Since $\cos Y=\frac{7}{25}$, we have $\cos Y=\frac{Y Z}{X Y}=\frac{Y Z}{25}=\frac{7}{25}$. From this, we can see that $Y Z=25 \cdot \frac{7}{25}=7$. Then, from the Pythagorean Theorem, $X Z=\sqrt{X Y^{2}-Y Z^{2}}=\sqrt{25^{2}-7^{2}}=\sqrt{576}=24 .$ Finally, we have tan $X=\frac{Y Z}{X Z}=$

Final Answer: The final answer is $\frac{7}{24}$
by Diamond (71,587 points)

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