If you have a 900cm2 plane mirror 45 cm in front of you and can just see the full length of an 8.5m flagpole behind you how far are you from the flagpole?

To answer this, you need the height H of the mirror, not its area. Are we supposed to assume it is a squate mirror? In that case, H = 30 cm

If H is the length of the mirror in the vertical direction,
H/0.45 = 8.5/(X +0.45)

Solve for X, once you know H.

42

To determine your distance from the flagpole, we can use the concept of similar triangles. Here's how you can calculate it step by step:

1. Let's assume that you are standing in front of the plane mirror with your back facing the flagpole. Draw a diagram to visualize the situation.

2. The mirror is placed 45 cm in front of you, and we know that the area of the mirror is 900 cm². However, the area of the mirror is not directly relevant to this problem, so we can ignore it for now.

3. Stand in front of the mirror and note the height of the flagpole that is visible to you through the mirror.

4. Since the mirror creates an identical virtual image of the flagpole, the height of the flagpole in the mirror will be the same as the actual height of the flagpole.

5. Now, let's use the concept of similar triangles. The height of the flagpole in your view is 8.5m. We need to find the distance between you and the flagpole, which we will represent as "x".

6. In the similar triangles formed by the flagpole, you, and the mirror, we can set up a proportion between the corresponding sides:

(height of flagpole) / (distance to flagpole) = (height in mirror) / (distance to mirror)

8.5m / x = 8.5m / 45cm

7. Convert the units to be consistent. Since the height of the flagpole is in meters, we need to convert the distance to the mirror from centimeters to meters.

8.5m / x = 8.5m / 0.45m

8. Simplify the equation:

1 / x = 1 / 0.45

9. Solve for x by taking the reciprocal of both sides of the equation:

x = 0.45

Therefore, you are approximately 0.45 meters away from the flagpole.