5.8 Right Triangle Trigonometry
The Pythagorean Theorem
I.SectionObjectives
- Identify and employ the Pythagorean Theorem when working with right triangles.
- Identify common Pythagorean triples.
- Use the Pythagorean Theorem to find the area of isosceles triangles.
- Use the Pythagorean Theorem to derive the distance formula on a coordinate grid.
II.ProblemSolvingActivity-TheRampDilemma
- For this problem, students will be using the Pythagorean Theorem to figure out whether or not the following
dimensions work for a bike ramp. They will be using the concept of Pythagorean triples in their work. - Here is the problem.
- “Jonas is building a bike ramp. He has a pattern for a small model of a bike ramp and he wants to build a
larger version of the bike ramp for his yard. His pattern uses measurements in inches. The pattern says that
the dimensions of the bike ramp model will be 9− 12 −15. Jonas wants to enlarge this pattern. Use what you
have learned about the Pythagorean Theorem and Pythagorean Triples to design a bike ramp that is not larger
than 21 feet−28 feet−34 feet.” - Solution Notes:
- This problem requires several steps. The first thing that the students are going to need to do is to convert feet
into inches. Then they will know how many inches the ramp design needs to be. - Next, the students need to begin to build proportions that work for triples.
- By multiplying by three, the students will find that they can build several different ramps.
- Here are some options:
- 27− 36 − 45 , 81 − 108 − 135
- The largest one without going over is 243− 324 − 405.
- Students need to draw a design with a scale to show their ramp.
- Then they need to write the final dimensions in feet.
- In feet- 20^14 − 27 − 3334 feet.
III.MeetingObjectives
- Students will use the Pythagorean Theorem in designing a bike ramp.
- Students will use their knowledge of Pythagorean triples in designing their ramp.
- Students will draw a design to show their work.
- The design will be drawn to scale.
IV.NotesonAssessment
- See the problem solving activity section for notes and solutions.
5.8. Right Triangle Trigonometry