Matt shadow is 8ft tall and he is only 5 ft tall. A flag pole has a 40ft tall shadow. How tall is the flag pole

To solve this problem, we can use the concept of similar triangles. The height and shadow of Matt and the flagpole form two right-angled triangles, and these triangles are similar, meaning their corresponding sides are proportional.

Given:
- Matt's height = 5 ft
- Matt's shadow = 8 ft
- Flagpole's shadow = 40 ft

Let \( h \) be the height of the flagpole.

We can set up the proportion based on corresponding sides:
\[
\frac{\text{Matt's height}}{\text{Matt's shadow}} = \frac{\text{Flagpole's height}}{\text{Flagpole's shadow}}
\]
\[
\frac{5}{8} = \frac{h}{40}
\]

Now, solve for \( h \):
\[
h = \frac{5}{8} \times 40 = 25 \text{ ft}
\]

Thus, the flagpole is 25 feet tall.

Would you like more details on solving proportions or have any other questions?

Here are 5 related questions to further your understanding:
1. How would the solution change if Matt's shadow was shorter, say 6 feet?
2. What are the properties of similar triangles that allow us to use this method?
3. How can you apply this method to find the height of a building using its shadow?
4. What if the flagpole had a shadow of 60 feet? How would the height change?
5. Can this method be used when the sun is at a different angle?

**Tip:** When using proportions, always ensure the corresponding parts of the figures (e.g., heights, shadows) are aligned correctly in the ratio.

Matt's shadow is 8ft tall and he is only 5ft tall. A flagpole has a 40ft tall shadow. How tall is the flagpole?

Learn how to use proportions and similar triangles to calculate the height of a flagpole. Given Matt's height of 5ft and his 8ft shadow, this method is used to find that the flagpole with a 40ft shadow is 25ft tall. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation