Essentials of Mathematics 10 - Trigonometry

This sub-organizer contains the following sections:
Prescribed Learning Outcomes
Suggested Instructional Strategies
Suggested Assessment Strategies
Recommended Learning Resources

PRESCRIBED LEARNING OUTCOMES

It is expected that students will demonstrate an understanding of ratio and proportion and apply these concepts in solving triangles

It is expected that students will:

• apply ratio and proportion in similar triangles
• use the trigonometric ratios sine, cosine, and tangent in solving right triangles

SUGGESTED INSTRUCTIONAL STRATEGIES

The study of trigonometry, starting with similar triangles, enables students to solve many ratio, proportion, and distance problems as well as problems that require determining the lengths of sides of triangles and the measure of unknown angles. These skills are particularly useful for construction trades such as carpentry.

Similar Triangles

• Have students draw (possibly using dynamic geometry software) a triangle in which two of the angles are between 10° and 60°. Ask them to:
  • avoid using a 30°-60°-90° triangle
  • draw the base horizontally
  • label the base a, and the sides b and c (clockwise)
  • label the corresponding angles A, B, and C
    Have them draw a second triangle larger than the first, where the angles of the new triangle are equal to the angles of the previous triangle, and label the new triangle a’, b’, and c’. Have students draw a line segment, perpendicular to the bases, that ends at A and A’, and label it D.
• Have students fill in a data table comparing all aspects of the two triangles; the measures of the angles, ratio of corresponding angles, lengths of the sides and their corresponding ratios, and the ratio of the areas of the two triangles. Ask them to draw conclusions about the relationships between the two triangles.

Trigonometry

• Have students use calculators or tables to find sine, cosine, and tangent for angles from 5° to 85° in 5° jumps. Have them compare the values from their previous tables for the 30° and 60° measures. Point out that the ratios of the lengths of the sides are what make up the values found in trigonometry tables or calculators.
• Demonstrate how to find the length of an unknown side (when given an angle and the length of one side) using derivations of the basic trigonometry formulas.
• Have students solve problems in real-world contexts that illustrate how knowledge of similar triangles and solving right triangles are useful skills (e.g., simple navigation problems, calculating inaccessible measurements such as the width of a river).

SUGGESTED ASSESSMENT STRATEGIES

Assessment focuses on students’ understanding of the basic properties of similar triangles and applications of their properties. Assessment of students’ comprehension of trigonometry should focus on their ability to use sine, cosine, and tangent to solve simple right triangle problems.

Observe

• Review students’ work as they draw, label, and measure the components of right triangles. Note their ability to label correctly and use protractor, calculator, and trigonometry table (or drawing utility) effectively. Look for proper use and function of calculators.

Question

• Ask students to explain or demonstrate the processes they used to solve similar triangle questions. Note the extent to which they are able to describe the ratios involved and their usefulness.

Collect

• Have students create tables of values that relate the lengths of sides of right triangles to angles for triangles they have drawn. Evaluate students’ ability to find unknown lengths and angles using direct measure and to calculate using the basic trigonometry identities.
• Collect students’ solutions to problems involving right triangles. Assess to what extent students are able to justify their answers.
• Ask students to solve right triangle problems and note the extent to which they are able to draw, label, and show the calculations leading to their answers.

Self Assessment

• Have students develop a study guide to solving problems using similar triangle ratios or trigonometry. Ask students to describe when and how to use the information in the guide (e.g., when to use sine or cosine when solving problems). Ask them to describe strategies that worked as well as those that did not.

RECOMMENDED LEARNING RESOURCES

Comprehensive learning resources for this course are currently under development. As an interim measure, schools are encouraged to use the teacher-developed learning resources distributed to schools (student and teacher resources). Please note that the student materials require photocopying for student use.

Print Materials

• Exploring Trigonometry with the Geometer’s Sketchpad

Software

• The Geometer’s Sketchpad

© 2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 22, 2000

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