We are given a right triangle with hypotenuse $c = 10$ and one leg $b = 6$. We need to find the length of the other leg, $a$.

1. Problem Description

We are given a right triangle with hypotenuse $c = 10$ and one leg $b = 6$. We need to find the length of the other leg, $a$.

2. Solution Steps

We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have:

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

We are given $b = 6$ and $c = 10$, so we can plug these values into the equation:

$a^2 + 6^2 = 10^2$

$a^2 + 36 = 100$

Now we can solve for $a^2$:

$a^2 = 100 - 36$

$a^2 = 64$

Finally, we take the square root of both sides to find $a$:

$a = \sqrt{64}$

$a = 8$

3. Final Answer

$a = 8$