Question

In \(\triangle X Y Z, \angle Z=90^{\circ}, \cos Y=\frac{7}{25}\), and \(X Y=25 .\) What is \(\tan X ?\)

Answer 1

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 \(\frac{7}{24}\)