Parking lot problem: Characterize the angle of a vehicle in a parking lot such that if we consider the length of the car as unit 1 and width of vehicle as x, with x ________________ | |...../\ | |......\ \ |_|____\ /__ angle theta in this corner In assigning a line segment of length 1 starting from the right front corner of vehicle, you could assign new variables along the left side of vehicle, that are cut by the temporary line segment as r and s. Then sqrt(x^2+r^2) + sqrt(s^2-x^2) = 1, r+s=1, (r=1-s) Short exercise would show x = sqrt(2s -1) -> s=(x^2+1)/2 The angle that is a complement of theta would thus be acos(x/((x^2+1)/2)) and so theta=asin(2 x/(x^2+1)) Graphing this shows from x=0 to x=1, the angles starts off at x=0 at the point (x,theta)=(0,0) with a slope of 2 and tapers off at the point (1,pi/2) where the limit of the slope for x=1 - is 1. Fascinating! What happens beyond 1 is immaterial to the problem. It looks similar to the dorsal fin of a shark....