Page 145 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

2.2 determine, through investigation using a variety of tools (e.g., calculators, dynamic geometry software, manipulatives) and strat- egies (e.g., modelling; making a table of values; graphing), the optimal dimensions of a two- dimensional shape in metric or imperial units for a given constraint (e.g., the dimensions that give the minimum perimeter for a given area)
Sample problem: You are constructing a rec- tangular deck against your house. You will use 32 ft of railing and will leave a 4-ft gap in the railing for access to stairs. Determine the dimensions that will maximize the area of the deck.
2.3 determine, through investigation using a vari- ety of tools and strategies (e.g., modelling with manipulatives; making a table of values; graphing), the optimal dimensions of a right rectangular prism, a right triangular prism, and a right cylinder in metric or imperial units for a given constraint (e.g., the dimensions that give the maximum volume for a given surface area)
Sample problem: Use a table of values and a graph to investigate the dimensions of a rec- tangular prism, a triangular prism, and a cylinder that each have a volume of 64 cm3 and the minimum surface area
By the end of this course, students will:
3.1 solve problems in two dimensions using metric or imperial measurements, including problems that arise from real-world applica- tions (e.g., surveying, navigation, building construction), by determining the measures
of the sides and angles of right triangles using the primary trigonometric ratios, and of acute triangles using the sine law and the cosine law
3.2 make connections between primary trigono- metric ratios (i.e., sine, cosine, tangent) of obtuse angles and of acute angles, through investigation using a variety of tools and strategies (e.g., using dynamic geometry software to identify an obtuse angle with
the same sine as a given acute angle; using
a circular geoboard to compare congruent triangles; using a scientific calculator to com- pare trigonometric ratios for supplementary angles)
3.3 determine the values of the sine, cosine, and tangent of obtuse angles
3.4 solve problems involving oblique triangles, including those that arise from real-world applications, using the sine law (in non- ambiguous cases only) and the cosine law, and using metric or imperial units
Sample problem: A plumber must cut a piece of pipe to fit from A to B. Determine the length of the pipe.
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3.5 gather, interpret, and describe information about applications of trigonometry in occupa- tions, and about college programs that explore these applications
Sample problem: Prepare a presentation to showcase an occupation that makes use of trigonometry, to describe the education and training needed for the occupation, and to highlight a particular use of trigonometry in the occupation.
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Pipe
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115° 5􏰁
3. Solving Problems Involving Trigonometry
GEOMETRY AND TRIGONOMETRY
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Foundations for College Mathematics
MAP4C