## Saturday, March 15, 2008

### Vicky's Pythagoras Growing Post

Part 1
Pythagorean Triple:

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.

This is a perfect square chart from 1 squared to 10.

The Pythagorean Theorem states that the legs (a and b) and the hypotenuse (c) Also a squared must be the lowest number, and c must be the highest number. A right triangle obey the following relationship----> A2+B2=C2

Two other examples of Pythagorean Triple, using 6, 8, 10.

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Part 2
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

Missing Leg

This is what we know
a squared= ? squared
b squared= 32 squared
c squared= 40 squared

The formula is a + b = c
a + 32 squared = 40 squared
a + 1024 = 1600

To get a squared we need to subtract 32 squared (b) from 40 squared (c).

c-b=a
40 squared - 32 squared = a squared
1600 - 1024 = a
a = 576
576 = 24 squared

a squared= ? squared
b squared= 32 squared
c squared= 40 squared

Missing Hypotenuse

This is what we know
a squared = 96 squared
b squared = 128 squared
c squared = ? squared
Formula is a + b = c
96 squared + 128 squared = c squared
9216 + 16384 = c
c = 25600
25600 = 160 squared

a squared = 96 squared
b squared = 128 squared
c squared = 160 squared

Pythagorean Triple Chart
3 squared + 4 squared = 5 squared
6 squared + 8 squared = 10 squared
12 squared + 16 squared = 20 squared
24 squared + 32 squared = 40 squared
48 squared + 64 squared = 80 squared
96 squared + 128 squared = 160 squared
192 squared + 256 squared = 320 squared
384 squared + 512 squared = 640 squared

The pattern is to multiply each term by 2.

Other Pythagorean Triple Chart I have found online

( 3, 4, 5)
( 5, 12, 13)
( 7, 24, 25)
( 8, 15, 17)
( 9, 40, 41)
(11, 60, 61)
(12, 35, 37)
(13, 84, 85)
(16, 63, 65)
(20, 21, 29)
(28, 45, 53)
(33, 56, 65)
(36, 77, 85)
(39, 80, 89)
(48, 55, 73)
(65, 72, 97)

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).

First circle all the important numbers, and underline all the important facts, to keep us organize.

Next draw a diagram of the question, and use the information that we've accumulated to label the appropriate areas.

Now use the pythagorean theorem to solve the missing side
The missing side is the hypotenuse.
What we know
a = 1.3m (0.7m - 2m)
b = 1.5m
c = ?m
Here is the pythagorean theorem
a squared + b squared = c squared
1.3m squared + 1.5 squared = c squared
1.69m + 2.25m = c squared
3.94m = c squared
3.94m square root = c squared square root
3.94m square root = c
1.98 = c (use a calculator, square root of 3.94)

a = 1.3m
b = 1.5m
c = 1.98m

Part 4: Now that you have seen many Pythagorean problems, create your own word problem.
Mizz Froggy stands 8.9 m from the wall where a fly is 8 m high. If the frogs tongue comes out of his mouth 10 cm from the ground, how far does his tongue have to stretch to trap and eat the fly?

#### 1 comment:

judy817 said...

wow. =o great start to your growing post!