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To find the height \( h \) of the triangular base, we can apply the Pythagorean Theorem. The base is an equilateral triangle with side lengths of 180 meters. By dividing the triangle into two right triangles, we know the following:

- Each right triangle has a base of half of 180 meters, so \( \frac{180}{2} = 90 \) meters.
- The hypotenuse of the right triangle is 180 meters (one side of the equilateral triangle).
- The height \( h \) is the missing side.

Using the Pythagorean Theorem:
\[
h^2 + 90^2 = 180^2
\]
Now, solving for \( h \):
\[
h^2 + 8100 = 32400
\]
\[
h^2 = 32400 - 8100 = 24300
\]
\[
h = \sqrt{24300} \approx 155.9 \, \text{meters}
\]

Thus, the height \( h \) of the triangular base is approximately **155.9 meters**.

Would you like more details, or do you have any questions?

Here are some related questions you might consider:
1. How is the area of an equilateral triangle calculated using the height?
2. How would the Pythagorean Theorem change if the triangle were not equilateral?
3. How do you find the height of an isosceles triangle with different side lengths?
4. What is the significance of dividing an equilateral triangle into two right triangles?
5. How does the triangular prism's height (25 m) affect the total volume?

**Tip:** The Pythagorean Theorem is applicable only to right-angled triangles, so when dealing with non-right triangles, other methods such as the Law of Cosines may be needed.

Find the height h of the triangular base. The base is an equilateral triangle with 180 meters on each side.

Learn how to find the height of an equilateral triangle with a side length of 180 meters by applying the Pythagorean Theorem. This guide breaks down the steps and provides a detailed solution, perfect for high school geometry students.

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