Answer
$x=8.66$ feet
Work Step by Step
Graph $f(x)=\arctan{\left(\frac{15}{x}\right)}-\arctan{\left(\frac{5}{x}\right)}$ using a graphing utility, then identify its maximum point.
Refer to the graph below.
Thus, the value of $x$ that maximizes the viewing angle is $8.66$.
Therefore, the student must sit next to the wall $8.66$ feet from the front of the classroom to maximize his viewing angle.
