We are given a right triangle with hypotenuse 10 cm and one leg 8 cm. We need to find the length of the other leg, which is labeled $x$.

1. Problem Description

We are given a right triangle with hypotenuse 10 cm and one leg 8 cm. We need to find the length of the other leg, which is labeled $x$.

2. Solution Steps

We can use the Pythagorean theorem to solve for $x$. The Pythagorean theorem states that for a right triangle with legs $a$ and $b$ and hypotenuse $c$, we have:

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

In this case, we have $a = x$, $b = 8$, and $c = 10$. Plugging these values into the Pythagorean theorem, we get:

$x^2 + 8^2 = 10^2$

$x^2 + 64 = 100$

$x^2 = 100 - 64$

$x^2 = 36$

$x = \sqrt{36}$

$x = 6$

3. Final Answer

$x = 6$ centimeters.