Thursday, March 13, 2008

Jessica Q's Pythagoras Growing Post

What is a Pythagorean Triple?
A Pythagorean Triple is 3 perfect unknown numbers used to satisfy:
a² + b² = c²
Example of a Pythagorean Triple:
using 1² - 10² on the perfect square chart

a² + b² = c²
6² + 8² = 10²
(6² = 6x6, 8² = 8x8, 10² = 10x10)
a² = 36 (6x6)
b² = 64 (8x8)
c² = 100 (10x10)

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=?)

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).

Worksheet A:
You’re locked out of your house and the only open window is on the 2nd floor 25 feet above the ground. You need to borrow a ladder from one of your neighbors. There’s a bush along the edge of the house, so you’ll have to place the ladder 10 feet from the house. What length of the ladder do you need to reach the window?

What I did in this word problem was, I drew a triangle which also showed the house, the ladder, and the ground. The ground and the house were the legs and the ladder was the hypotenuse. Since the question asks us to find out the length of the ladder, I used the theorem, “a²+b²=c²”. The given numbers so far were “10² feet” and “25² feet”. 10² and 25² are the legs of the triangle. After, I had to find the square root of these numbers. (10²=100 and 25²=625) I added up the numbers 100 and 625 to find out was c was. (625+100=725) Now that I had my answer, I found out what the square root of 725 was, which was 26.93². 26.93² is the length of the ladder needed to reach the window of the house.

Part 4:
Julie drives from her house to work. She starts at her house, drives 9 km south, then 12 km east to her work. How far is Julie's work from her house?

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