To find the value of \(\frac {AD}{BE}\), we'll use the given information about the angles in \(△ ABC\) and the properties of altitudes.
Let's start by labeling the triangle and its angles:
\(∠BAC = 45°\)
\(∠ABC = θ\)
Now, let's draw altitudes AD and BE:
Angle \(\angle BAE = 45°\) degrees is stated.
This suggests \(AE = BE\).
Suppose \(AE = BE = x\).
It is written as \(\angle{ABC}=\theta\) in the right-angled \(△ ABD\).
\(sin\theta=\frac{AD}{AB}\)
\(sin\theta=\frac{AD}{x\sqrt{2}}\)
\(\sqrt2sin\theta=\frac{AD}{BE}\)
\(\frac{AD}{BE}=\sqrt2sin\theta\)
So, the correct option is (A): \(\sqrt2sin\theta\)