The problem asks to find the height $h$ of an equilateral triangle, given that the base of the triangle is 10.

1. Problem Description

The problem asks to find the height $h$ of an equilateral triangle, given that the base of the triangle is

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0.

2. Solution Steps

Since the triangle is equilateral, all sides are equal in length. The height bisects the base, creating two right triangles. The base of each right triangle is half of the base of the equilateral triangle, which is $10/2 = 5$. The hypotenuse of each right triangle is the side length of the equilateral triangle, which is

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0. We can use the Pythagorean theorem to find the height $h$.

$a^2 + b^2 = c^2$

where $a$ and $b$ are the legs of the right triangle and $c$ is the hypotenuse.

In this case, $a = 5$, $b = h$, and $c = 10$.

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

$25 + h^2 = 100$

$h^2 = 100 - 25$

$h^2 = 75$

$h = \sqrt{75}$

$h = \sqrt{25 \times 3}$

$h = \sqrt{25} \times \sqrt{3}$

$h = 5\sqrt{3}$

3. Final Answer

$h = 5\sqrt{3}$