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

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 2

make it less confusing

Answer 3

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 4

make a picture

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.