## Monday, March 17, 2008

### Kadille Dave's Pythagoras Growing Post

1) A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime. The name is derived from the Pythagorean theorem, of which every Pythagorean triple is a solution. The converse is not true. For instance, the triangle with sides a = b = 1 and c = √2 is right, but (1, 1, √2) is not a Pythagorean triple because √2 is not an integer. Moreover, 1 and √2 don't have an integer common multiple because √2 is irrational.

If (a, b, c) is a Pythagorean triple,is (ka, kb, kc) for any positive integer k. The name is derived from the Pythagorean theorem, of which every Pythagorean triple is a solution.

a=3x3
b=4x4
c=5x5

a+b=c

9+16=25

2)Find The Missing Side

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3) School Problem Mr. H jumped into a canoe to cross a river. That runs east to west and is 20m wide. The current carried him downstream 8m before he reach the other side. How did he travel in total?

Given: 20m= edge to edge of the river
8m= downstream effect
c= mr. H travelled

This looks how the problem talks about.

solution on how to solve the problem

4) Own Problem

Angelo is planning to slide on a mountain that has a measurement of 156 meters from end to end. There is a building at the summit 10 meters wide and eight meters high. The center of the building is standing exactly on the summit of the building. The summit of the mountain is in the center of the mountain. If someone travel from the summit to the base of the mountain, he will travel 100 metres. The starting point is where the edges of the building is. Find how high did Angelo start sliding?

This diagram shows the labels of sides or measurements in the problem.

The real missing side is from the starting point down to the base of the mountain.
-but the other sides of the triangle are not the exact ones
-there is a building on top of the mountain

letter points
z-distance from the summit to the end of the mountain

Z-the distance from the starting point to the ground that is measured using the slope.

c-distance from the summit to the edge of the mountain.

H - the height of the mountain from the summit down to the base

h- the distance on how high Angelo started sliding from the ground

Q- the distance of the edges of the mountain divided into 2 minus 5

P=Starting Points

plan:
to solve the exact missing sides using: ratio and proportion, subtracting, dividing, and finding the missing side

1. Ratio and Proportion - solve for c
The angle of the small triangle inside the building has the same angle as the whole triangle from one end

H - the height of the mountain from the summit down to the base
it has a measurement of 62.58 metres

2. Solve for z

3. Solve for Q

Lastly, solve the problem. Because we got the exact measurement of the given sides

a-h(?)
b-q
c-Z

Solution
(click the picture to enlarge)