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.