Question

 A movie projector positioned 34 feet from a wall creates an image that is 8 feet wide on the wall. if a screen is placed 5 feet in front of the projector, what will the width of the image be on the screen

Answer 1

Answer: 1.48ft

Step-by-step explanation:

The angle, θ, at which the projector "spreads" the image is constant.

We know that:

"A movie projector positioned 34 feet from a wall creates an image that is 8 feet wide on the wall"

We can think this problem as the image in the end, two triangle rectangles with cathetus equal to 34 ft, and 8/2 ft = 4ft

Then this angle θ can be calculated because we know the two cathetus of this triangle:

Tan(θ) = (opposite cathetus)/(adjacent cathetus)

Tan(θ) = 4ft/34ft

θ = Cotan(4/34) = 8.46°

Now, if you move the place the projector 5ft from the wall, now the adjacent cathetus is 5ft instead of 34.

Then we have:

Tan(8.46°) = x/5ft

Tan(8.46°)*5ft = x = 0.74ft

But remember that the actual width of the image will be two times that, so the width is:

W = 2*0.74ft = 1.48ft