Finding the value of theta using the $6$ trigonometric functions on an $xy$ plane. Here's a link of what I am trying to learn about. 
http://www.webpages.uidaho.edu/learn/math/lessons/lesson03/3_05.htm
Now I have one question. How will I find the value for theta in each function if the hypotenuse has no exact square root and is now a decimal.
Let $(14,5)$ be a point on the terminal side.
$x = 14$
$y = 5$
\begin{align*}
r & = \sqrt{14^2+5^2}\\
r & = \sqrt{196+25}\\
r & = \sqrt{221}\\
r & = 14.86
\end{align*}
What do I need to do with the calculator?    

Based on a now deleted comment, it is my understanding that the terminal side of the angle passes through the point $(14, 5)$.  You used the Pythagorean Theorem to conclude correctly that $r = \sqrt{221}$.  

Using the trigonometric formulas
\begin{align*}
\sin\theta & = \frac{y}{r} & \csc\theta & = \frac{r}{y}\\
\cos\theta & = \frac{x}{r} & \sec\theta & = \frac{r}{x}\\
\tan\theta & = \frac{y}{x} & \tan\theta & = \frac{x}{y}
\end{align*}
with the values $x = 14$, $y = 5$, and $r = \sqrt{221}$ yields the exact values
\begin{align*}
\sin\theta & = \frac{5}{\sqrt{221}} & \csc\theta & = \frac{\sqrt{221}}{5}\\
\cos\theta & = \frac{14}{\sqrt{221}} & \sec\theta & = \frac{\sqrt{221}}{14}\\
\tan\theta & = \frac{5}{14} & \tan\theta & = \frac{14}{5}
\end{align*}
Now that we have the exact values, we can plug them into the calculator to obtain the approximations
\begin{align*}
\sin\theta & \approx 0.34 & \csc\theta & \approx 2.97\\
\cos\theta & \approx 0.94 & \sec\theta & \approx 1.06\\
\tan\theta & \approx 0.36 & \cot\theta & = 2.8
\end{align*}
where I have rounded to the nearest hundredth except for $\cot\theta$.  The value for $\cot\theta$ is exact. 
