What’s the Angle?



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What’s the Angle?


Diane Leighty

Powhatan County Public Schools


Developed with funding from the American Council of Engineering Companies of Virginia and the MathScience Innovation Center




Question(s)

What makes two figures similar? How does the angle of the flag in the Iwo Jima statue compare with the angle of the Marine Museum building itself? To the spire that originates at the center of the Leatherneck Gallery inside the museum?




Grade/Subject

Grade 6, 7, 8 Mathematics
Virginia Standards of Learning: 2009 Math 6 (6.12, 6.13); 2009 Math 7 (7.6); 2009 Math 8 (8.3)




21st Century Curriculum

Engineering: Design and Build (2.22), Civil Engineering (4.45)




Background

Engineers design and build products in response to human needs, incorporating specific details that are relevant to that project. The building that houses the National Museum of the Marine Corps at Quantico is said to be inspired by the Iwo Jima Statue of the soldiers raising an American flag. This lesson is an opportunity to explore just how similar these two structures are. The angled spire that goes from the Leatherneck Gallery inside the museum up through the roof measures 210 feet.




Materials

  • Ruler (metric)

  • Protractor

  • Handout with scaled drawings




Safety

Students should observe the usual safety rules that were established at the beginning of the year, including being careful with measuring devices.




Procedure

  1. Start with the handout that contains the picture of the Iwo Jima Statue and the angled spire that originates inside the museum and extends out the roofline.



  2. Measure the angles created by each image.



  3. Take the handout that contains pictures of the statue and the museum structure. Draw a right triangle that captures the statue and its shape.



  4. Measure the angles and the sides of your created triangle. Enter these measurements in the table below.



  5. Repeat steps 4 and 5 with the photo of the Marine Museum building, using the angled spire rather than the roofline as one side of the triangle. You will need to use your ruler to extend the line from the top of the spire to the base of the building.




Data Analysis / Results

How do the angles compare from step 2 of the procedure?


Data Table: Comparison of Angles


Object

Angle 1

Angle 2

Angle 3

Side 1

Side 2

Side 3

Iwo Jima Statue







90°










Marine Museum







90°









Compare the pictures based on the measurements you took. What similarities, if any, are there between the photos?


Compare the ratios of corresponding sides. Are they the same, almost the same, or very different?
If the actual length of the spire is 210 feet, what is the scale factor between the photo and the real spire?







Conclusion / Questions

Are any of these objects similar? Explain your reasoning.





References

The official website of the National Museum
http://www.usmcmuseum.org/
The Marine Corps Heritage Foundation
http://www.marineheritage.org/
Consulting Engineers: Hankins & Anderson, http://www.haengineers.com/

Jacobs Engineering, http://www.jacobs.com/


MathScience Innovation Center
Information on educational programs available to students, teachers and school divisions and procedures for registering for programs.
http://msinnovation.info


Student Handout:
Part 1: Measure the angles

Iwo Jima Statue Marine Museum at Quantico



Part 2: Create a right triangle and measure the parts.

What’s the Angle? http://MathInScience.info ©MathScience Innovation Center, 2011



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