A 6-ft tall man notices his shadow is 4 feet long. At the same time of day, he measures the shadow of a nearby water tower and finds it to be 19.2 feet long.

 

How tall is the water tower?

To find the height of the water tower, we can use the concept of similar triangles. The man's height and his shadow form one right triangle, and the height of the water tower and its shadow form another similar right triangle.

### Step-by-Step Solution

1. **Identify the ratios of corresponding sides in similar triangles:**

   Since the triangles are similar, the ratio of the man's height to his shadow length is the same as the ratio of the water tower's height to its shadow length.

2. **Set up the proportion:**

   Let \( h \) be the height of the water tower.

   \[
   \frac{\text{man's height}}{\text{man's shadow length}} = \frac{\text{water tower's height}}{\text{water tower's shadow length}}
   \]

   Plugging in the given values:

   \[
   \frac{6}{4} = \frac{h}{19.2}
   \]

3. **Solve for \( h \):**

   Cross-multiply to solve for \( h \):

   \[
   6 \times 19.2 = 4 \times h
   \]

   \[
   115.2 = 4h
   \]

   Divide both sides by 4:

   \[
   h = \frac{115.2}{4} = 28.8
   \]

4. **Conclusion:**

   The height of the water tower is **28.8 feet**.

Would you like more details on any part of this solution or have any questions? 

### Related Questions:

1. If the man's shadow was 5 feet long instead, what would the height of the water tower be?
2. What is the height of an object if its shadow is 8 feet long, given the same conditions?
3. How would the solution change if the ground was not level and flat?
4. If the shadow of the water tower changed to 21 feet, what would be the new height of the tower?
5. What are some real-life applications of similar triangles in geometry?

**Tip:** When dealing with similar triangles, remember that corresponding sides are proportional, which allows you to set up a simple ratio to solve for missing lengths.

Learn how to calculate the height of a water tower using similar triangles with a detailed step-by-step solution. Understand the concept of proportions and apply it to find the unknown height of the water tower based on shadow lengths. Suitable for Grades 7-9 students.

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