NY Regents Geometry case studies
NY Regents Geometry · Put your knowledge to work in context.
The Geometry Regents Examination is a New York State Regents exam in mathematics, administered through the New York State Education Department (NYSED), which lists Regents Exams among its Assessments and the Next Generation Learning Standards among its Popular Topics. It is intended for New York high school students who have completed a geometry course aligned to the state's mathematics standards. The exam samples the six content domains shown on this page: Congruence; Similarity, Right Triangles, and Trigonometry; Circles; Expressing Geometric Properties with Equations; Geometric Measurement and Dimension; and Modeling with Geometry. Expect proof-based reasoning alongside coordinate geometry, circle relationships, volume and surface area, and applied modeling tasks. The NY Regents Geometry case studies are 5 cases and about 2,778 words.
1Two Triangular Stage Braces with a Non-Included Angle
A community theater is rebuilding two triangular side braces for a revolving set. Brace ABC has AB = 7.0 ft, BC = 5.0 ft, and angle A = 38°.
583 words, about 3 min2Wheelchair Ramp Slope, Post Height, and Handrail Length
A community center is building a wheelchair ramp to a door 2.4 ft above the sidewalk. The available horizontal distance is 30 ft.
569 words, about 3 min3Circular Window Chord, Inscribed Angles, and Tangent Strip
A stained-glass studio is designing a circular window of radius 3.0 ft. A straight brass bar will be installed as chord AB, with AB = 4.2 ft.
533 words, about 3 min4Triangular Park Path and Fountain Circle on a Coordinate Map
A city planning map uses a coordinate grid measured in hundreds of feet. A triangular park has vertices A(-4, 1), B(6, 3), and C(2, 9).
602 words, about 3 min5Cylinder-and-Hemisphere Silo Capacity and Paint Order
A farmer is replacing a grain silo made of a right circular cylinder with a hemispherical roof. The cylinder has radius 6.0 ft and height 18.0 ft; the hemisphere sits on top with the same radius.
491 words, about 2 min