Calculate the BD:AC Ratio in a Right Triangle with Median to Hypotenuse

To solve this problem, we'll follow these steps:

• Step 1: Recognize that triangle ABC is a right triangle with BD as the median to the hypotenuse AC.
• Step 2: Apply the geometric property that the median to the hypotenuse of a right triangle is half the length of the hypotenuse.

Now, let's work through these steps:
Step 1: The problem states that BD is the median to the hypotenuse AC in the right triangle ABC.
Step 2: According to the geometric property of a median in a right triangle, the length of the median BD is half the hypotenuse $AC$. Therefore, $BD = \frac{1}{2}AC$.

Thus, the ratio between $BD$ and $AC$ can be expressed as:
$\frac{BD}{AC} = \frac{\frac{1}{2}AC}{AC} = \frac{1}{2}$
This simplifies to the ratio $1:2$.

Therefore, the solution to the problem is $1:2$.