Finding the length of a line drawn from the right angle to the hypotenuse.

Question

I'm supposed to find the length of the line drawn from a point on the hypotenuse of a right triangle to the right angle. Obviously I'm able to find line AB but that doesn't help me find AD as far as I can tell.

I thought about the Alternate interior angles rules but they apply to parallel lines.

A little difficult to google search for the answer due to the nature of the question.

Any explanation is greatly appreciated.

Question

Answer 1

Use the fact that the area of triangle $ABC$ is $\frac 12\times AB\times AC$, but it is also $\frac 12\times AD\times BC$.

Answer 2

If $A$ is the right angle and we drop a perpendicular $AD$ to $BC$, then $\triangle ABD \sim \triangle ABC$; thus

$\dfrac{AD}{AB} = \dfrac{AC}{BC} \tag 1$

or

$AD = \dfrac{(AB)(AC)}{BC}. \tag 2$