Page 52 - Math 9-10 (2009)

PRINCIPLES OF MATHEMATICS, GRADE 10, ACADEMIC (MPM2D) 51
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;
• solveproblemsinvolvingacutetriangles,usingthesinelawandthecosinelaw.
Specific Expectations
Investigating Similarity and Solving Problems Involving Similar Triangles
By the end of this course, students will:
– verify, through investigation (e.g., using dynamic geometry software, concrete materials), the properties of similar trian- gles (e.g., given similar triangles, verify the equality of corresponding angles and the proportionality of corresponding sides);
– describe and compare the concepts of similarity and congruence;
– 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 navi- gating, in determining the height of an inaccessible object around the school), using the primary trigonometric ratios and the Pythagorean theorem.
Solving Problems Involving the Trigonometry of Acute Triangles
By the end of this course, students will:
– explore the development of the sine law within acute triangles (e.g., use dynamic geometry software to determine that the ratio of the side lengths equals the ratio of the sines of the opposite angles; follow the algebraic development of the sine law and identify the application of solving systems of equations [student reproduction of the development of the formula is not required]);
– explore the development of the cosine law within acute triangles (e.g., use dynamic geometry software to verify the cosine law; follow the algebraic development of the cosine law and identify its relationship to the Pythagorean theorem and the
opposite
hypotenuse