# Question #b1a21

##### 2 Answers

That is correct. See explanation.

#### 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:

So

Rewriting everything, we have:

We take the derivative of

because the derivative of

Rearranging, we get:

i.e.:

i.e.:

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:

i.e.

i.e.

(because we omit the answer that is negative since we are talking about a distance, which is always positive).

Q.E.D.

See below.

#### Explanation:

We have

but

then

which occurs for

and then

NOTE