To find the distance between the points \((0,0)\) and \((36,15)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (36, 15)\).
Substituting the coordinates into the formula gives:
\[ d = \sqrt{(36 - 0)^2 + (15 - 0)^2} \] \[ d = \sqrt{36^2 + 15^2} \]
Calculating \(36^2\) and \(15^2\):
\[ 36^2 = 1296 \] \[ 15^2 = 225 \]
Adding these values together:
\[ 1296 + 225 = 1521 \]
Now, taking the square root:
\[ d = \sqrt{1521} = 39 \]
Thus, the distance between the points \((0,0)\) and \((36,15)\) is \(\boxed{39}\).