This is a math problem which you can explore
on Geometer Sketch Pad.
Along with seeing how I did the problem, you can play around with it too!
1. Imagine that you are hanging a picture on your wall.
You have hung the picture so that its base is two feet above eye level.
You want people to get a proper look at the painting.
* How far away from the painting must they stand in order to get the best view?
* Can we assume that closer is better ? Maybe they will get a better view if they back up a lot?
2. You are now having second thoughts about how you hung your painting and you want to try hanging it up higher or lower so that you can get the best possible view.
* At what height should you put your painting to optimize your viewing angle?
Explore problem 1 Explore problem 2 Solution to Problem 1 Solution to Problem 2
* How far away from the painting must they stand in order to get the best view?
* Can we assume that closer is better ? Maybe they will get a better view if they back up a lot?
2. You are now having second thoughts about how you hung your painting and you want to try hanging it up higher or lower so that you can get the best possible view.
* At what height should you put your painting to optimize your viewing angle?
Explore problem 1 Explore problem 2 Solution to Problem 1 Solution to Problem 2