# Calculus

#### LordDevn

##### New member
(problem below)I've set up the equation by using the law of cosines.
Cos (t) = (385+xx)/((121+xx)^(1/2)(xx+1225)^(1/2)) but it is incorrect....I did this by using the pathagoren theory to get the two sides other than 24 ft given...Can someone tell me where I went wrong on setting up the equation?

A movie screen on a wall is 24 feet high and 11 feet above the floor. At what distance from the front of the room should you position yourself so that the viewing angle of the movie screen is as large as possible?

#### happy

##### Full Member
hey can you show humakhan how to post images attachments,thanks

#### LordDevn

##### New member
happy said:
hey can you show humakhan how to post images attachments,thanks
Who is Humakhan??but anyway it is easy....Just right click the image you see and hit copy image location....Then paste the location in your reply and highlight it....next click the img button at the top of the page and it will be copied inside your post when you preview or post it.

#### soroban

##### Elite Member
Hello, LordDevn!

I've set up the equation by using the law of cosines.
. . . cos θ .= .(x<sup>2</sup> + 385) / (x<sup>2</sup> + 121)<sup>1/2</sup> (x<sup>2</sup> + 1225)<sup>1/2</sup>

but it is incorrect ... I did this by using the Pythagoren theory to get the two sides other than 24 ft given
Can someone tell me where I went wrong on setting up the equation?
I checked your result . . .

. . . . . . . . . . . b<sup>2</sup> + c<sup>2</sup> - a<sup>2</sup>
. . cos A . = . ---------------
. . . . . . . . . . . . . 2bc

In this problem: . A = θ, .b = (x<sup>2</sup> + 121)<sup>1/2</sup>, .c = (x<sup>2</sup> + 1225)<sup>1/2</sup>, .a = 24

. . . . . . . . . . . . . . . . . . . .(x<sup>2</sup> + 121) + (x<sup>2</sup> + 1225) - 576
So we have: . cos θ . = . ---------------------------------------
. . . . . . . . . . . . . . . . . . . . 2(x<sup>2</sup> + 121)<sup>1/2</sup>(x<sup>2</sup> + 1225)<sup>1/2</sup>

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .x<sup>2</sup> + 385
which simplifies to: . cos θ . = . -<u>-----------</u>--<u>-------------</u>-
. . . . . . . . . . . . . . . . . . . . . . . . .√x<sup>2</sup> + 121 √x<sup>2</sup> + 1225

. . . and I found absolutely nothing wrong with your work!

[Question: How do you know that it's wrong?]

#### LordDevn

##### New member
Soroban...It is a problem for my online HW and I plugged in my numbers and it tells me i'm incorrect.

#### soroban

##### Elite Member
Hello, LordDevn!

It is a problem for my online HW and I plugged in my numbers and it tells me i'm incorrect.
Did you differentiate the function . . . carefully?
. . . And solve for x?

It took me two tries to get it, but I finally nailed it down.
. . . . . . . . . . . . . ___
Answer: . x .= .√385 .= .19.62141687... feet

#### pka

##### Elite Member
Here is another way to set the problem using the arctangent function.
It gives the same answer as Soroban found.

Lovely, pka!

#### LordDevn

##### New member
Thank you to both of you for your help and time....Your answers are correct but for some reason it says the equations are wrong....It might just be a clitch in the computer system or it may be something sensitive, i've emailed my instructor about it...Again thank you for your time.

#### LordDevn

##### New member
Sorban and pka....this is just an update that the original thought on the problem was right....turns out their was something wrong with the system when I plugged in the equation.