Need to determine distance maximizing angle theta.

[Hellsing834]

Homework Statement

A movie screen at the front of a room is 9 feet above the ground and 16 feet tall. Determine the distance X you must sit away from the screen in order to maximize your viewing angle.

[ I tried to make the picture :P. I need to find X]

http://img50.imageshack.us/img50/2781/probwk6.png The little fish thing is i believe alpha...i don't know the Greek name for that.

Homework Equations

Well i figured that i need to do the tangent of both triangles and set them equal to each other, but i am confused if i need to take into account the second triangle for tan of theta.

I am comming up empty handed, and what i got was 25/tan[theta] but i don't think its right.

 

[Hellsing834]

help...anyone? i kinda need desperate help :P

 

[Mark44]

Good drawing! And, yes, that Greek letter is alpha.

What you need is an equation with theta as a function of x.

First, let's take care of alpha: cot(alpha) = x/9, so alpha = cot^(-1)(x/9).

Next, let's get a relationship between the larger angle and x.

tan(theta + alpha) = 25/x
so theta + alpha = tan^(-1)(25/x)

But we already have alpha, so you should be able to get theta as a function of x; i.e., theta = f(x).

Now, do the usual and find d(theta)/dx and set it equal to 0.

Does that get you started?