The altitude of a right angle (and its children)
- Ryan Hirst
In a right triangle, let the altitude from the right angle cut the hypotenuse into two segments. Then the square of the altitude is equal to the product of the two segments.
If we let AC = 1, we can draw any of the relationships among a given angle α and the lengths sin²(α), cos²(α), sin(α)cos(α): http://www.geogebratube.org/material/show/id/30937 (To apply these relationships to an arbitrary right triangle, scale them by the length of the hypotenuse.)