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Soccer Problem(1)

  • Soccer Problem

    Grade: High School

    A soccer player is on a breakaway, dribbling the ball downfield, parallel to a sideline. From where should she shoot to have the best chance of making a goal? That is, at what point will the angle formed by the player and the two goal posts be the greatest?

    The applet below allows you to investigate this problem by changing the location of the player as well as the distance between the player and the goal posts. As you move the player, the angle changes. Where should the player be placed so that the angle is maximized?

     

    Activity

     
    Copyright © 2016 KCP Technologies, a McGraw-Hill Education Company. All rights reserved.
    Release: 2015Q4Update1, Semantic Version: 4.5.0, Build Number: 1012.2-r, Build Stamp: ip-10-149-70-76/20160225151924

    Instructions

    • Adjust how far player C is from the the goal by dragging Point C along the light blue dotted line.
    • The Show/Hide Circle buttons allow you to create a circle that will help solve the problem.
      • The radius of the circle can be modified by dragging the black point on the slider labeled, radius of circle.
      • Drag the circle around the workspace by its center point.
       

    Exploration

    Drag point C so that the angle is as large as possible along that breakaway line.

      Click Show Circle. Where should the circle be placed, and what should its radius be so that Player C has the best chance of making a goal? What is the relationship between point P and the circle?

        Objectives and Standards

        NCTM Standards and Expectations
        • Geometry / Measurement
        • Functions and Trigonometry
        • Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
        • High School (9-12)
        • Geometry
        • Measurement