Page 55 - Math 9-10 (2009)

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THE ONTARIO CURRICULUM, GRADES 9 AND 10: MATHEMATICS
Measurement and Trigonometry
Overall Expectations
By the end of this course, students will:
• use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity;
• solveproblemsinvolvingrighttriangles,usingtheprimarytrigonometricratiosandthe Pythagorean theorem;
• solveproblemsinvolvingthesurfaceareasandvolumesofthree-dimensionalfigures,and use the imperial and metric systems of measurement.
Specific Expectations
Solving Problems Involving Similar Triangles
By the end of this course, students will:
– verify, through investigation (e.g., using dynamic geometry software, concrete materials), properties of similar triangles (e.g., given similar triangles, verify the equality of corresponding angles and the proportionality of corresponding sides);
– determine the lengths of sides of similar triangles, using proportional reasoning;
– solve problems involving similar triangles in realistic situations (e.g., shadows, reflec- tions, scale models, surveying) (Sample problem: Use a metre stick to determine the height of a tree, by means of the simi- lar triangles formed by the tree, the metre stick, and their shadows.).
Solving Problems Involving the Trigonometry of Right Triangles
By the end of this course, students will:
– determine, through investigation (e.g., using dynamic geometry software, con- crete materials), the relationship between the ratio of two sides in a right triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios (e.g.,
sin A = );
– determine the measures of the sides and angles in right triangles, using the primary
trigonometric ratios and the Pythagorean theorem;
– solve problems involving the measures of sides and angles in right triangles in real- life applications (e.g., in surveying, in navigation, in determining the height of an inaccessible object around the school), using the primary trigonometric ratios and the Pythagorean theorem (Sample problem: Build a kite, using imperial measurements, create a clinometer to determine the angle of elevation when the kite is flown, and use the tangent ratio to calculate the height attained.);
– describe, through participation in an activity, the application of trigonometry in an occupation (e.g., research and
report on how trigonometry is applied in astronomy; attend a career fair that includes a surveyor, and describe how a surveyor applies trigonometry to calculate distances; job shadow a carpenter for a few hours, and describe how a carpenter uses trigonometry).
Solving Problems Involving Surface Area and Volume, Using the Imperial and Metric Systems of Measurement
By the end of this course, students will:
– use the imperial system when solving measurement problems (e.g., problems involving dimensions of lumber, areas of carpets, and volumes of soil or concrete);
opposite
hypotenuse