Expert: Scotto - 2/10/2009

Question
A camera on a h = 5 foot high tripod is placed in front of a m1 = 7 foot high picture that is mounted m2 = 3 feet above the floor as shown in the figure below. (Note: Figure is not drawn to scale.)


(a) Express angle θ as a function of the distance x from the camera to the wall. (Use asin for sin-1, acos for cos-1, and atan for tan-1 as needed.)
θ =

(b) The photographer wants to use a particular lens, for which θ = 30° (π/6). How far should she place the camera from the wall to be sure that the entire picture will show in the photograph? (Round your answer to two decimal places.)



PICTURE (http://img.photobucket.com/albums/v384/peaches323/mATH3.gif)


I tried a couple ways, but none of them worked..

ANS in FEET

Answer
The angle Θ should be so that the camera looks into the middle
if the image.  Let the distance from the picture me d.
The picture is 7 feet high and therefore has a middle at 3.5 feet
above the bottom.

The bottom is a 3 feet off the floor, so the center of the picture
is 3+3.5 = 6.5 feet off the floor.

(a) THe distance away is x.  The camera is at height 5.
THe distance the picture above the camera is 6.5 - 5 = 1.5 feet.
The angle the camera needs to be pointing to is given by
tan(Θ) = 1.5/x.

(b) If the camera is set at 30°, take tan(30°) = 1.5/x and
solve for x.  You know, x = 1.5/tan(30°).

I'm not sure I will even try the picture this time since again,
it is not necessary.