A five foot boy casts a two foot shadow at the same time the shadow of the  court house tower is 25 feet in length how tall is the court house tower

To solve this problem, we can use the concept of similar triangles. The boy and his shadow form one triangle, and the courthouse tower and its shadow form another. Since the sun's rays are at the same angle for both, the triangles are similar, and we can set up a proportion.

Let's define:
- The height of the boy as \( h_b = 5 \) feet,
- The length of the boy's shadow as \( s_b = 2 \) feet,
- The height of the courthouse tower as \( h_t \) (which we need to find),
- The length of the courthouse tower's shadow as \( s_t = 25 \) feet.

The proportion can be set up as follows:

\[
\frac{h_b}{s_b} = \frac{h_t}{s_t}
\]

Substituting the known values:

\[
\frac{5}{2} = \frac{h_t}{25}
\]

Now, solve for \( h_t \) by cross-multiplying:

\[
h_t = \frac{5 \times 25}{2} = \frac{125}{2} = 62.5 \text{ feet}
\]

So, the height of the courthouse tower is **62.5 feet**.

Would you like further details on this solution, or do you have any questions?

Here are 5 related questions for further exploration:
1. How does the concept of similar triangles help in solving real-world problems?
2. If the boy's shadow was longer, how would it affect the height of the tower?
3. What happens to the length of shadows as the sun moves throughout the day?
4. Can this method be used to find the height of a mountain using its shadow?
5. How would you solve this if you had a different set of measurements?

**Tip:** When working with proportions, always ensure the units are consistent across the ratio to avoid errors.

Learn how to calculate the height of a courthouse tower using the concept of similar triangles. Given the height and shadow length of a boy, and the shadow length of the tower, find the tower's height step-by-step. Suitable for students in Grades 6-8.

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