A right triangle has a segment from the right angle that meets the hypotenuse at a right angle at point p. Point p splits the hypotenuse into two segments whose lengths are 16 units and 4 units. Find the distance from the perpendicular line to the right angle
Since the line segment from point P meets the hypotenuse at a right angle and the hypotenuse is the longest side of a right triangle, we can conclude that triangle PBC is a right triangle.
Let the distance from the perpendicular line to the right angle be x units.
Using the Pythagorean theorem in triangle PBC, we have:
x^2 + 4^2 = 16^2
x^2 + 16 = 256
x^2 = 256 - 16
x^2 = 240
x = sqrt(240)
x ≈ 15.49
Therefore, the distance from the perpendicular line to the right angle is approximately 15.49 units.