Sally's Path
Situation
From Sullivan's Pre-Calculus. Sally is running from House 1 ( ) to House 2 ( ). She runs along the beach to a point on the paved sidewalk, then crosses the bridge, continues on the sidewalk, and then cuts across the beach at the same angle as before. Show that the angle is at least .
Applet
The slide a controls where Sally arrives on the sidewalk. The path and thus, the angle, changes according. Since there is water between the two house, she must cross at the Bridge (the origin). What angle will result if she stays entirely on the beach except when she crosses at the bridge? Move the slider to find out.