## Thursday, March 13, 2008

### Derrick's Pythagoras Growing Post

- Pythagorean Triple ?
- Three numbers a, b, and c that satisfy a2 + b2 = c2 are called Pythagorean Triples.
- some Pythagorean triple other than 3,4,5 is 5,12,13

This picture shows how a pythagorean triple works. Its three squares making a right angle triangle in the middle.

Example:

Following the formula a2 + b2 = c2 we got 5² +12² = 13².

a²= 5 - 5²
b²= 12 - 12²
c²= 13 - 13²

a2 + b2 = c2
5² +12² = 13²
25 + 144 = 169

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?

PART III

In this problem, it says to find the length of the ladder to reach the window. (Ladder: a, house: b, ground: c) In the picture, you can see a triangle. (a²+b²=c²) The length between the window to the ground is 25 feet, the length between the house to the ladder is 10 feet because of the bush, you have to find how long the ladder has to be. (25²+10²=c²) Next you have to find the square root of these numbers. (25² = 625, 10² = 100) An easy way to find the length of the ladder is just by adding the square roots together. (625+100=725) Then, you have to find the squared number of 725. (√725 = 26.93²) Now that you have the square root of 725, 26.93 feet is how long the ladder has to be to reach the window.

PART IIII
Jordan and Jon are playing a 2 on 1 volleyball game with Jessica. Jessica served the ball to Jordan with a distance of 12 m. Then Jordan passed the ball to Jon with a distance of 5 m. How far does Jon have to hit the ball to Jessica?