Sam wants to find the height of a window in a

nearby building but it is a cloudy day with no
shadows. Sam puts a mirror on the ground
between himself and the building. He tilts it
toward him so that when he is standing up, he
sees the reflection of the window. The base of
the mirror is 1.22 meters from his feet and 7.32
meters from the base of the building. Sam’s eye
is 1.82 meters above the ground. How high up
on the building is the window?

Idk the answer

To find the height of the window, we can use similar triangles formed by Sam, the mirror, and the building.

Step 1: Identify the lengths and distances given in the problem:
- Base of the mirror (distance from Sam's feet): 1.22 meters
- Distance from the base of the mirror to the base of the building: 7.32 meters
- Height of Sam's eye from the ground: 1.82 meters

Step 2: Draw a diagram to visualize the situation:
```
_________________________
| |
| |
| |
| |
| |
| |
| |
|_________________________|
^ Sam's eye
Reflecti |_________________________
on of | |
Sam | |
__| |
| |
| |
| |
| |
| |
|_________________________|
Base of the mirror
(Sam's feet)
```

Step 3: Determine the ratios of the corresponding sides of the similar triangles:
The ratio of corresponding sides in the triangles formed by Sam's eye, the top of the window, and the top of the mirror will be the same as the ratio of their corresponding sides in the triangles formed by Sam, the mirror, and the building.

The corresponding sides we will use are:
1. Height of the building window (let's call it "h")
2. Height of the mirror (1.22 meters)
3. Height from Sam's eye to the top of the mirror (1.82 meters)

So, we have the ratio: (h/1.22) = (1.82/1.22)

Step 4: Solve for "h":
To find the height of the building window ("h"), we can cross-multiply and solve for "h":
h = (1.82/1.22) * 1.22
h = 1.82 meters

Therefore, the height of the window on the building is 1.82 meters.

To find the height of the window on the building, we can use similar triangles and the properties of angles of incidence and reflection.

Let's break down the given information:
- The distance between Sam's feet and the base of the mirror is 1.22 meters.
- The distance between the base of the mirror and the base of the building is 7.32 meters.
- Sam's eye is 1.82 meters above the ground.

Here's how we can solve for the height of the window:
1. Draw a diagram to represent the situation. Label the distances and heights mentioned in the question.

| O Sam's Eye (1.82m)
| |
|----------------- ------------
| | |⁄
| |h | /
| | |⁄ Mirror
|---------- |------------ Building
Sam's d h
Feet (7.32m)

2. Identify the similar triangles. The small triangle formed by Sam's feet (base), the mirror's base, and the height of the mirror is similar to the larger triangle formed by Sam's eye, the mirror's base, and the height of the building.

Small Triangle: Sam's Feet - Mirror's Base - Mirror's Height
Large Triangle: Sam's Eye - Mirror's Base - Building's Height

3. Set up the proportion between the corresponding sides of the similar triangles.

(Mirror's Height) / (Sam's Feet - Mirror's Base) = (Building's Height) / (Sam's Eye)

h / 1.22 = (h + d) / 1.82

4. Cross-multiply and solve for h, which represents the height of the window.

1.82h = 1.22(h + d)
1.82h = 1.22h + 1.22d
0.6h = 1.22d
h = (1.22d) / 0.6

5. Substitute the given distance between the mirror's base and the building's base.

h = (1.22 * 7.32) / 0.6

6. Calculate the value of h to find the height of the window.

h ≈ 14.96 meters

Therefore, the height of the window on the building is approximately 14.96 meters.

I don't think you can answer the question without knowing how much the mirror had to be tilted.

If the mirror is tilted an angle x, and the angle θ from the normal is formed by the ray from eye to mirror to window, then we have (if the height of the window is h):

1.82/1.22 = tan(π/2-θ-Ø)
h/7.52 = tan(π/2-θ+Ø)

Maybe I'm missing something?