Answer:
[tex] \displaystyle \sec( \theta) = \frac{25}{7} [/tex]
Step-by-step explanation:
remember that,
[tex] \displaystyle \sec( \theta) = \frac{hypo}{adj} [/tex]
since we aren't given hypo we can consider Pythagoras theorem given by
[tex] \displaystyle {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] \displaystyle \implies c = \sqrt{ {a}^{2} + {b}^{2} }[/tex]
substitute the value of a and b:
[tex] \displaystyle c = \sqrt{ {7}^{2} + {24}^{2} }[/tex]
simplify squares:
[tex] \displaystyle c = \sqrt{49 + 576}[/tex]
simplify addition:
[tex] \displaystyle c = \sqrt{625}[/tex]
simplify square root:
[tex] \displaystyle c = 25[/tex]
with respect to [tex]\theta[/tex] adj is 7 and hypo is 25 thus
substitute:
[tex] \displaystyle \sec( \theta) = \frac{25}{7} [/tex]
and we are done!