Introduction
Hello, we will be exploring ways engineers, architects, and construction crews can use geometry every day to build walkways, bridges, ramps, homes, and more.
Let us say that you have been hired as junior engineers to assist with building projects throughout Mississippi. To determine missing measurements, you have to use the Pythagorean Theorem along with special right triangles. Your objective is to submit a final engineering report as a reflection.
Task
You will investigate three engineering projects and determine the missing measurements. For each project, explain how you found your answer.
Project 1
Wheelchair Ramp Design
A school is building a wheelchair ramp.
The ramp forms a right triangle with a horizontal distance of 24 feet and a vertical distance of 7 feet.
- Questions
- What is the length of the ramp?
- Why is the ramp the hypotenuse?
- Would a longer ramp create a steeper or less steep incline?
Project 2
Roof Construction
A contractor is designing a roof support.
The support beam forms a 45-45-90 triangle, with the hypotenuse measuring 14 feet.
- Questions
- What is the length of the other legs?
- Why are the legs the same?
Project 3
City Park Walkway
A city park contains a baseball field-shaped garden such that one section forms an equilateral triangle and the other forms a semicircle.
Each side of the equilateral triangle portion of the garden measures 18 feet.
A walkway is built such that it forms a vertical line of symmetry.
- Questions
- Given the construction of the walkway, what type of special right triangle is formed?
- What is the length of the walkway?
Final Engineering Report
Create a presentation addressing the following questions:
- Which project was most interesting and why?
- How can recognizing a special right triangle make solving problems easier?
- When should engineers use the Pythagorean Theorem?
Process
For each individual, I would suggest the following steps necessary to complete this task:
- Review this video that introduces trigonometry and the Pythagorean theorem:
- Read Chapter 8: Right Triangles (pg. 80 - 85) via the Geometry Handbook and review the following videos elaborating on the topic:
- Once you complete the engineering report, review what you have learned:
Evaluation
The content of this topic will be evaluated through the Test Yourself link to Quizizz.
Conclusion
For this webquest, students were tasked to act within a STEM role as they completed public projects. Finally, students were given a quiz to test their understanding