A tree casts a shadow 8m long. At the same time a 2-m wall casts a shadow 1.6m long.
a) Sketch a diagram.
b) What is the height of the tree?
From the grade 9 Math Makes Sense text book, p352
Questions to consider:
1. Is it practical?
It is somewhat practical.
2. Is it memorable?
Not really.
3. Is it solvable?
Yes it is.
4. Can it be interpreted in more than one way?
Yes, the tree and wall might be close enough that one can ask if the shadow of the tree is partially on the wall, it doesn’t mention anything about the shadow being on a flat surface, like the ground for example.
5. Is it strange in any way?
No it’s not extremely strange, but it’s a rather dry problem.
6. How would you extend the problem?
To make the problem somewhat memorable, it would be nice to involve some human aspect to the problem. For example a younger brother and an older brother standing next to each other on a sunny day, and the younger brother wants to know how tall his brother is.
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