The length of LP is 57.73.
Since a line perpendicular to other line forms a 90 angle, we can use the Pythagorean theorem to solve the problem.
LM² = NP² + MP²
We know LM = 20 and we can see that NP = MN = 30, so we can substitute the known values into the equation.
20² = 30² + MP²
20² = 900 + MP²
MP² = 20² - 900
MP² = 400
MP = √400
MP = 20
Since we have a right triangle with two known sides, we can use the tan function to solve for LP.
LP = tan(m∠KLM) * MP
LP = tan(126°) * 20
LP = 57.73
Therefore, the length of LP is 57.73.