- Students will understand the different parts of right triangles.
- Students will use the tangent ratio in a right triangle.
- Students will identify complementary angles in right triangles.
- Students will understand tangent ratios in special right triangles.
IV.NotesonAssessment
- Walk around as the students are working.
- Notice which students are having difficulty and offer support.
- Allow students time to share their work when finished.
Sine and Cosine Ratios
I.SectionObjectives
- Review the different parts of right triangles.
- Identify and use the sine ratio in a right triangle.
- Identify and use the cosine ratio in a right triangle.
- Understand sine and cosine ratios in special right triangles.
II.ProblemSolvingActivity-Dion’sYardDesign
- Here is the problem.
- “Dion has a square yard. He wants to divide the yard on the diagonal by planting a beautiful row of fruit trees.
The yard measures 16×16. If this is the case, what is the measurement of the diagonal? Draw a diagram of
the yard and the diagonal to also answer the following questions about the ratios in the yard.” - Students begin by drawing a diagram of the yard.
- Using the Pythagorean Theorem, the diagonal is 22.6 feet long.
- Now use these measurements to answer the following questions.
- What is sina?
- What is sinb?
- What is cosa?
- What is cosb?
- Solutions:
- 1425
- 2.. 7
- 3.. 7
- 4.. 7
- Allow time for the students to share their work at the end.
- Extension: Would the ratios be the same if the diagonal extended the opposite way as well?
III.MeetingObjectives
- Students will review the different parts of right triangles.
- Students will identify and use the sine ratio in a right triangle.
- Students will identify and use the cosine ratio in a right triangle.
IV.NotesonAssessment
- Check the student diagram first.
5.8. Right Triangle Trigonometry