100Right triangle, tan from cos

In right triangle $\displaystyle XYZ$, angle $\displaystyle Z$ is the right angle and $\displaystyle \cos X = \frac{8}{17}$. What is the value of $\displaystyle \tan X$? A) 8/15 B) 15/17 C) 15/8 D) 17/8

tan X = 15/8, answer (D). With cos X = 8/17, the adjacent side is 8 and hypotenuse 17; the Pythagorean theorem gives the opposite side as 15, so tan X = opposite/adjacent = 15/8.