Girl in the Mirror - similar triangles
- Author:
- OER Offline, Markus Hohenwarter
{{TAGLINE}} How large does a mirror need to be to see your full body?
{{LO}} The learning objective is to learn the application of similar triangles and triangle formulae to solve a real-world problem.
{{SC}} You have developed a mathematical expression that determines the size of the mirror.
{{BEFORE}} Discuss the question posed: How large does a mirror need to be to see your full body? Have you wondered about this before? What might the size of the mirror depend on? What can you determine about this problem in advance?
{{TASK}} Now move on to the GeoGebra task, using the applet below. Move the girl and use the checkboxes to provide some clues. If you are sharing the device, take turns to use the applet. What determines the size of the mirror? Does person's distance from the mirror matter? Does the person's height matter? Can you figure out a relationship drawing on similar triangles?
{{AFTER}} What has the task shown you? Can you now make a diagram that shows how to determine the size of the mirror needed? What does the size depend on? What does it not depend on? As an extension, consider how does the mirror needs to be positioned. Can you develop a formula?
Once you have developed the mathematical expression, what does it tell you about the real world? Consider this: What if you had a family, with different heights? How large would the mirror need to be, and how would you place it on the wall?