The screen of a pin-hole camera is a square, of side 0.16m and it is 0.15m behind the pinhole. The camera is placed 11m from a flag staff and positioned so that the image of the

flag is formedd centrally on the screen.
The image occupies three quarters of the height of screen.
What is the height of the flag staff?

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To find the height of the flagstaff, we need to determine the height of the image on the screen and then use similar triangles to calculate the height of the flagstaff.

First, let's find the height of the image on the screen:
Given that the image occupies three-quarters of the height of the screen, we can say that the height of the image is:

image_height = (3/4) * screen_height

Since we know the side length of the screen is 0.16m, we can substitute this into the equation to find the height of the image:

image_height = (3/4) * 0.16m

Simplifying this expression, we get:

image_height = 0.12m

Now, let's use similar triangles to calculate the height of the flagstaff.
In a pin-hole camera, the ratio of the object distance to the image distance is equal to the ratio of the object height to the image height.

The object distance is the distance from the camera to the flagstaff, which is given as 11m. The image distance is the distance from the pinhole to the screen, which is given as 0.15m.

We can set up the proportion:

object_distance / image_distance = object_height / image_height

Substituting the values:

11m / 0.15m = flag_height / 0.12m

Simplifying this expression, we get:

(11m * 0.12m) / 0.15m = flag_height

Solving for flag_height, we get:

flag_height = 8.8m

Therefore, the height of the flagstaff is 8.8 meters.

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