What is the height of the flag staff if a pinhole camera is placed 11m away the screen is .16 m square .15m behind the pinhole. The image is centered and three-quarters of the height of the screen?

Answer 1

Assuming the image is parallel to the flag-pole:

The scale factor is 0.15 m : 11 m = 1 : 11/0.15

The height of the image is ¾ of 0.16m = ¾ × 0.16 m = 0.12m

→ the flag-pole is 0.12m × 11/0.15 = 8.8 m

Answer 2

Through no fault of your, there is an ambiguity in the question. I interpreted the screen size as being its area and so a screen with an area of 0.16 m square would have sides of 0.4 m. This gives a flag-staff which is 22 metres high. That is some tall flag staff!

However, as was pointed out to me by a colleague, 0.16 m square could also mean a screen which was 0.16 m x 0.16 m. This gives a scale factor that is 0.4 times as large and so the flag-staff would be a more credible 8.8 metres.