The task is asking to find the height of an equilateral triangle if the side length is 10.

For an equilateral triangle, the height can be calculated using the Pythagorean theorem. When we draw a height in an equilateral triangle, it splits the triangle into two right-angled triangles. The base of each right triangle is half the side length (i.e., 10/2 = 5), and the hypotenuse is the side of the equilateral triangle (10).

Let $h$ represent the height. Using the Pythagorean theorem:

$h^2 + 5^2 = 10^2$

Now, let's solve for $h$:

$h^2 + 25 = 100$

$h^2 = 100 - 25 = 75$

$h = \sqrt{75} \approx 8.66$

Thus, the height of the equilateral triangle is approximately 8.66 units.

Would you like more details on the process or have any questions about this? Here are some related questions to explore further:

1. How do you find the area of an equilateral triangle?
2. What is the relationship between the side length and height in any triangle?
3. How do you calculate the perimeter of an equilateral triangle?
4. Can the Pythagorean theorem be applied to all types of triangles?
5. How does the height change if the side length of the triangle is increased?

Tip: For any equilateral triangle, the height $h$ can also be found using the formula $h = \frac{\sqrt{3}}{2} \times \text{side length}$.