Question

A cell phone tower casts a 100-foot shadow. At the same time, a 4-foot 6-inch post near the tower casts a shadow of 3 feet 4 inches. How tall is the cell phone tower?

Answer 1

make it less confusing

Answer 2

make a picture

Answer 3

To solve this problem, we can use the principle of similar triangles.

Let’s denote:
- The height of the cell phone tower as \( h \).
- The height of the post as \( 4 \) feet \( 6 \) inches, which can be converted to feet. There are \( 12 \) inches in a foot, so \( 6 \) inches is \( \frac{6}{12} = 0.5 \) feet. Thus, the height of the post is \( 4 + 0.5 = 4.5 \) feet.
- The length of the shadow of the cell phone tower is \( 100 \) feet.
- The length of the shadow of the post is \( 3 \) feet \( 4 \) inches. Converting this to feet, \( 4 \) inches is \( \frac{4}{12} \approx 0.333 \) feet. So the shadow of the post is \( 3 + 0.333 = 3.333 \) feet.

By the property of similar triangles, we can set up the following proportion:

\[
\frac{h}{100} = \frac{4.5}{3.333}
\]

Now, we can solve for \( h \):

1. Cross-multiply:

\[
h \cdot 3.333 = 4.5 \cdot 100
\]

2. Calculate \( 4.5 \cdot 100 \):

\[
4.5 \cdot 100 = 450
\]

3. The equation now looks like this:

\[
h \cdot 3.333 = 450
\]

4. To find \( h \), divide both sides by \( 3.333 \):

\[
h = \frac{450}{3.333}
\]

5. Now, perform the division:

\[
h \approx 135
\]

Thus, the height of the cell phone tower is approximately **135 feet**.

Answer 4

Sure! Let's break it down step-by-step in a more straightforward manner:

1. **Identify the Heights and Shadows**:
- **Post Height**: 4 feet 6 inches = 4.5 feet
- **Post Shadow**: 3 feet 4 inches = 3.333 feet
- **Tower Shadow**: 100 feet
- **Tower Height**: Let’s call this \( h \).

2. **Set Up a Proportion**:
Since the post and the tower cast shadows in similar conditions, we can set up a proportion based on their heights and shadow lengths:

\[
\frac{h}{100} = \frac{4.5}{3.333}
\]

3. **Cross-Multiply**:
Now we will cross-multiply to find \( h \):

\[
h \times 3.333 = 4.5 \times 100
\]

This simplifies to:

\[
h \times 3.333 = 450
\]

4. **Solve for \( h \)**:
Now, divide both sides by 3.333:

\[
h = \frac{450}{3.333}
\]

5. **Calculate \( h \)**:
Doing the division gives us:

\[
h \approx 135 \text{ feet}
\]

**Final Answer**: The height of the cell phone tower is approximately **135 feet**.

Answer 5

I'm unable to create or display images directly in this format, but I can help you visualize how to draw a simple diagram.

### How to Draw the Diagram

1. **Draw the Post**:
- Draw a vertical line to represent the post. Label it "Post: 4.5 ft".

2. **Draw the Post's Shadow**:
- Draw a horizontal line extending from the base of the post. This line represents the shadow of the post. Label it "Shadow: 3.333 ft".

3. **Draw the Tower**:
- Next to the post, draw a taller vertical line to represent the cell phone tower. Label it "Tower: h ft".

4. **Draw the Tower's Shadow**:
- Finally, draw a long horizontal line extending from the base of the tower for the shadow. Label this line "Shadow: 100 ft".

### Annotating the Diagram

- You can add a note to show the proportion:

\[
\frac{\text{Tower Height } (h)}{\text{Tower Shadow } (100)} = \frac{\text{Post Height } (4.5)}{\text{Post Shadow } (3.333)}
\]

### Example Layout

```
|
| (Tower: h ft)
|
|
____|______
| (Shadow: 100 ft)

_____ | _____
| | | | |
| Post| | | Post|
| | | | |
| 4.5 | | | 3.333|
| ft | | | ft |
|_____| | |_____|
```

This should give you a simple visual representation of the situation. If you're looking to create a computer-generated image, you might want to use illustration software or online graphing tools.