That is correct. See explanation.
First of all, we need to figure out the expression that relates
Let's call the observer's point O, the point on the wall along the horizontal line-of-sight (at the bottom of
So we have three triangles OPA and OAB, together forming OPB.
Let's also call the angle AOP
We know that:
Rewriting everything, we have:
We take the derivative of
because the derivative of
Rearranging, we get:
Set the derivative to zero and solve for x.
As you can see, the denominator is always positive, so, we only need to solve for the numerator to be zero.
In the numerator, we can factor out the
So, we are left with:
(because we omit the answer that is negative since we are talking about a distance, which is always positive).
which occurs for