You can draw a triangle with $\displaystyle{a}={8}\usepackage{cmbright}\Huge\$ and $\displaystyle{o}={7}\usepackage{cmbright}\Huge\$ . Then use the Pythagorean Theorem to find the length h, of the hypotenuse:

$\displaystyle{{8}}^{{2}}+{{7}}^{{2}}={{h}}^{{2}}\Rightarrow{64}+{49}={{h}}^{{2}}\Rightarrow{113}={{h}}^{{2}}\Rightarrow\sqrt{{113}}={h}\usepackage{cmbright}\Huge\$

Now use the definition of secant:

$\displaystyle{\sec{{X}}}=\frac{{h}}{{a}}=\frac{\sqrt{{113}}}{{8}}\usepackage{cmbright}\Huge\$