Saturday, March 15, 2008

Anne's Pythagoras Growing Post

Part 1: Describe what a Pythagorean Triple is and use your perfect square chart from 1 squared to 10 squared to find another one other than 3,4,5. (Note: You need a picture, not simply text.)

The definition that Mr. Jerema gave us was:
"A Pythagorean Triple is a right triangle that uses a set of whole numbers (1, 2, 3....etc) that satisfy A² + B² = C²"

A pythagorean Triple is a right triangle where the sides are in the ratio of a positive integer or whole number.
Examples are] 3:4:5, 6:8:10, 5:12:13, 9:12:15, 8:15:17 etc.
The formula is simple] a² + b² = c² OR x² + y² = z²
You can invert that formula with the examples like this] 3² x 4² = 5²

perfect square chart
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100

Part 2: Using embeddable web 2.0, describe how to find the missing side of a Right Triangle using the Pythagorean Theorem, show how to solve both for a missing leg and the hypotenuse (note: you may use numerical examples ie. a=4 b=6 c=?)

The first slides about the missing hypotenuse shows that the straight angle is 3 and the other straight angle is 4, is can be labelled either a or b. But let's say that a = 3 and b = 4. Now we have to find the missing side, since the right angle is in the bottom left corner, pretend to draw a little box to make sure that it is a right angle. Now if you can imagine the box, it would be pointing to the line.. which is the hypotenuse. We have to figure out what the hypotenuse is so we first:
write down what we already know
then write down the pythagorean thereom
then transfer that into the squared numbers
then transfer that into their standard form
then add it together and you get the number
but after you have to figure out the square unit for the number
in this case, the number is 25,
which is easy because the square unit is perfect since 5 squared = 25.

Part 3: Explain how to solve a Pythagoras word problem. Use one of the examples we covered in class (Worksheet A, B, LeFrog or Bonus Problem).

You've just picked up a ground ball at first base, and you see the other team's player runnig towards thrid base. How far do you have to throw the ball to get it from first base to thrid base, and runner out?

I highlighted half the square because it made a right triangle. Since all the sides are 90 squared except for the line running through third base and first base. That was the hypotenuse.

Part 4: Now that you have seen many Pythagorean problems, create your own word problem.

Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point?

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