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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
