Students will apply the concepts of angle bisector, incenter of a triangle, and percentages to solve a real-world problem involving a circular sprinkler and a triangular-shaped lawn.
Before the Activity
Students should have a basic understanding of angle bisectors, perpendicular lines, areas of triangles and circles, and percentages. Possible curricular placements include high school geometry or a geometry courses for pre-service or in-service teachers at the college level.
During the Activity
The Parks Department has purchased a new sprinkler whose spray rotates to form a perfect circle. The sprinkler is to water the triangular-shaped lawn that is surrounded by sidewalks. Where should the sprinkler be placed inside the triangular-shaped lawn so as to cover as much of the lawn as possible without spraying the sidewalks?