Answer:
5/4
Step-by-step explanation:
To do this you must know that by definition secant is:
[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex]
Furthermore:
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
Based on this information we know that 3 = opposite and 5 = hypotenuse. Assuming this is a right triangle we can determine the adjacent side by Pythagorean Theorem.
[tex]c^2=a^2+b^2[/tex]
Where c is the hypotenuse, a is adjacent and b is opposite. Therefore,
[tex]c^2=a^2+b^2\\\\a=\sqrt{c^2-b^2} \\\\a=\sqrt{5^2-3^2} \\\\a=4[/tex]
And so the adjacent side of this triangle is 4. Going back to the definition of secant we can now know that:
[tex]sec(\theta)=\frac{1}{cos(\theta)}=\frac{1}{\frac{4}{5}}=\frac{5}{4}[/tex]
