Page 75 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

C. GEOMETRY AND TRIGONOMETRY OVERALL EXPECTATIONS
By the end of this course, students will:
SPECIFIC EXPECTATIONS
By the end of this course, students will:
1.1 recognize and describe real-world applications of geometric shapes and figures, through investigation (e.g., by importing digital photos into dynamic geometry software), in a variety of contexts (e.g., product design, architecture, fashion), and explain these applications (e.g., one reason that sewer covers are round is to prevent them from falling into the sewer during removal and replacement)
Sample problem: Explain why rectangular prisms are often used for packaging.
1.2 represent three-dimensional objects, using concrete materials and design or drawing software, in a variety of ways (e.g., ortho- graphic projections [i.e., front, side, and top views], perspective isometric drawings, scale models)
1.3 create nets, plans, and patterns from physical models arising from a variety of real-world applications (e.g., fashion design, interior dec- orating, building construction), by applying the metric and imperial systems and using design or drawing software
1.4 solve design problems that satisfy given con- straints (e.g., design a rectangular berm that would contain all the oil that could leak from a cylindrical storage tank of a given height and radius), using physical models (e.g., built from popsicle sticks, cardboard, duct tape) or
drawings (e.g., made using design or drawing software), and state any assumptions made
Sample problem: Design and construct a model boat that can carry the most pennies, using one sheet of 8.5 in. x 11 in. card stock, no more than five popsicle sticks, and some adhesive tape or glue.
By the end of this course, students will:
2.1 solve problems, including those that arise from real-world applications (e.g., surveying, navigation), by determining the measures of the sides and angles of right triangles using the primary trigonometric ratios
2.2 verify, through investigation using technology (e.g., dynamic geometry software, spread- sheet), the sine law and the cosine law (e.g., compare, using dynamic geometry software,
the ratios a , b , and c in sinA sinB sinC
triangle ABC while dragging one of the vertices);
2.3 describe conditions that guide when it is appropriate to use the sine law or the cosine law, and use these laws to calculate sides and angles in acute triangles
2.4 solve problems that arise from real-world applications involving metric and imperial measurements and that require the use of the sine law or the cosine law in acute triangles
GEOMETRY AND TRIGONOMETRY
1. represent, in a variety of ways, two-dimensional shapes and three-dimensional figures arising from real-world applications, and solve design problems;
2. solve problems involving trigonometry in acute triangles using the sine law and the cosine law, including problems arising from real-world applications.
1. Representing Two-Dimensional Shapes and Three-Dimensional Figures
2. Applying the Sine Law and the Cosine Law in Acute Triangles
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Foundations for College Mathematics
MBF3C