Investigate the optimum position on the soccer field to score a goal.[br][br]A soccer player is running along a straight line toward the endline. Her path is perpendicular to the endline. She decides to try to shoot a goal when the angle θ that the goal subtends at her position is maximized. Click and drag the player to see how θ varies. How many feet y from the endline should she shoot? (All relevant distances, in feet, are shown in the diagram) [br][br]Now vary her line of approach, by moving the black point on the endline. [br][br]Can you find an expression that describes the optimal distance y from the endline in terms of the distance x?

Worksheet created by Keshav Mukunda.