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More Mini Orchards Before we start: Did you present your solution to HW #3 in class?Remember that presenting in class count as participation. As and Bs students always to get 100% in participation.Did you noticed that the solution to HW #3 is the midpoint of the hypotenuse of the right triangle? Did you mention that in your presentation? Back to the activity "More Mini Orchards." This activity is very similar to HW #2. Now you are asked to analyze orchards of radius 2 and 3. (2 and 3 trees in all directions) Remember that on HW # 2 the tree trunks touched each other to form a true "orchard hideout." Here is what you need to be able to solve these problems. I will also suggest that you take a good look at your hideout model from classwork #1 and read about the line of sight. Ready? 1. Read the activity one or twice. As you read take note of the information that you think will be useful to answer the questions. The first and second questions are very easy. 2. Get your graph paper and sketch the mini-orchards. Sketch each mini-orchard in each side of your paper. Remember, there is not tree in the center of the mini-orchards.
Materials needed for this classwork:
A copy of your hw
#3
Your reference
papers
Graph paper
(Don't have any? Get some
here)
Your compass
The definition of
Perpendicular Bisector and Equidistant
The Pythagorean
Theorem
Your Book
Suggestion: make your sketches fairly large and
to scale to facilitate their interpretation.
Do you know what drawing to scale really means?
3. After finishing both sketches read the
questions again.
Now, answer 1a, and 2a. Pretty easy, don't you
think?
How many trees are there in the radius 2
mini-orchard? ____________________
How many in the radius 3?
_________________________________________
To answer question 1b and 2b do the
following:
Go back to your sketches and label
everything on the first quadrant. (The right upper quarter of your sketch).
Remember: The distance between the center of
the mini-orchard and the center of the next tree to the right is one unit, etc.
In the radius two orchard
Where do you think the line of sight will be
this time?
How many options do you have this time?
Draw one of the possible lines of sight.
Now start drawing circle slightly bigger
around the center of the two closer trees.
Continue drawing circles until the one
touches, slightly the line of sight.
Since both trees are growing at the same rate they should be touching the line of sight at the same time.Would you be able to see the outside when both trunks touch the line of sight? Do the trunks need to be touching each other to become a true hideout? Explain. _________________________________________________________ How this situation differ from the orchard with only one tree? Are you ready to estimate the hideout tree radius for the orchard of radius 2? What is your estimation? __________________________________________ Is that radius bigger or smaller than the radius in the orchard with only one tree? Why? Follow the same procedure to approximate the hideout tree radius for the orchard of radius 3. How this radius compare to the previous one? Great job! You already answered the mandated questions. Are you ready for the challenge? To answer question three you should draw a new diagram showing only the trunks closer to the line of sight or better jet: Click the next link to find a sketch for the radius 2 orchard. doc pdf Complete the diagram and label its parts, then choose on of the following method to answer the question. Methods Using the Pythagorean theorem Using trigonometry Similarity and proportions Measuring Try more than one method to confirm your answer. Good luck! Please keep me inform of your progress. If you have any question please ask your teacher or contact me. Finally, you can get a sketch for the orchard of radius 3 by clicking here doc pdf Mr. Lora Under Construction
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