Question

what is \\( \tan \beta \\)?
\\( \tan \beta = \frac { \sqrt { ? } } { } \\)

Explanation:

Step1: Recall the formula for tangent in coordinate system

For an angle \(\beta\) in standard position with a point \((x,y)\) on its terminal side, \(\tan\beta=\frac{y}{x}\). Here \(x = 5\) and \(y=\sqrt{11}\).

Step2: Calculate \(\tan\beta\)

Substitute \(x = 5\) and \(y=\sqrt{11}\) into the formula \(\tan\beta=\frac{y}{x}\), we get \(\tan\beta=\frac{\sqrt{11}}{5}\). But the problem asks for the form \(\frac{\sqrt{?}}{?}\), and since \(\tan\beta=\frac{\sqrt{11}}{5}\), the number under the square - root is \(11\).

Answer:

\(11\)