The problem asks to find the radius of a circle given its equation in the form $(x-h)^2 + (y-k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius. The given equation is $(x-5)^2 + (y+8)^2 = 36$.

1. Problem Description

The problem asks to find the radius of a circle given its equation in the form $(x-h)^2 + (y-k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius. The given equation is $(x-5)^2 + (y+8)^2 = 36$.

2. Solution Steps

The general equation of a circle is:

$(x-h)^2 + (y-k)^2 = r^2$

where $(h, k)$ is the center and $r$ is the radius.

We are given the equation:

$(x-5)^2 + (y+8)^2 = 36$

Comparing this to the general form, we can see that:

$h = 5$

$k = -8$

$r^2 = 36$

To find the radius $r$, we take the square root of $r^2$:

$r = \sqrt{36}$

$r = 6$

3. Final Answer

The radius of the circle is 6.