**Pythagoras**is a very smart greek man, who was known that he made the pythagoras theory. He is a vegetarian and a teacher. He had figured out alot of things in his time of living, like for example, he found out that the earth revolved around the sun. He also has an interest in music. Although there was no evidence that he was real, stories were passed on to people.

This is the

**Pythagorean**

**theorem.**This theorem is believed to be invented by Pythagoras. We use this theorem to find out lengths of the right angle. We also use it to find the length of squares and rectangles.

The

**right triangle**is also called a R.A.T. meaning right angle triangle. The right triangle has a right angle that is 90 degrees. Theta and Beta are labeled on the two other sides of the right triangle. Theta is the symbol with an O and a line across and Beta is the symbol that looks like a B with a long tail. Both of the angles of Theta and Beta equal up to 90 degress, this is called complementry. Theta and Beta aren't always equally the same. The legs are labeled as 'a' and 'b', they are the angles of a 90 degree angle. (It doesnt matter which angle you label is 'a' or 'b' as long as they are labeled either.) The hypnotenuse is the longest line of a triangle and across from the triangle. The hypnotenuse is labeled as 'c'.

The

**square**has four 90 degree angles. This square is also called quadrilaterals meaning 4. The internal angle is 360 degrees. If you cut a square in half diagonally, you would get two right triangles. The lines on the square are called lines of symmetry. It shows you that all the lines are equal and that it is a square.

To solve this question, you have to use pythagoras.

First, we are looking for what is the length of b.

a²+b²=c²

We have to use the numbers we have and put them in the pythagorean theory.

8²+b²=10²

Now, you have to think about algebra, you have to isolate the b² in the equation.

b²=10²-8²

b²=(10x10)-(8x8)

b²=100-64

b²= 36

Then you have to square root both sides to get rid of the exponent.

The square root of b²=the square root of 36.

b=6

Now to find the whole bottom line, we must do this.

b=6mm

b+b=square root of _

6+6=12mm

Problem 2

A checkerboard is made of 64 small squares that each have a dimension of 3 cm x 3 cm. The 64 small squares are arranged in eight rows of eight.

A) What is the length of the diagonal of a small square? Give your answer to the nearest tenth of centimetre.

This question tells us that b and a are 3cm which means that you are going to find the answer to

c.

a²+b²=c²

3²+3²=c²

(3x3)+(3x3)=c²

9+9=c²

18=c²

Then we have to square root both sides to get rid of the exponent.

The square root of 18=the square root of c²

4.2=c

B) What is the length of the diagonal of the board? Give your answer to the nearest centimetre.

This question tells us that b and a are 8cm which means that you are going to find the answer to

c.

a²+b²=c²

8²+8²=c²

64+64=c²

128=c²

Then, we have to square root both sides of the equation to get rid of the exponent.

The square root of 128=the square root of c²

11.3=c

Video 1: Finding the Hypnoteuse. (c)

Video 2: Finding the legs. (a or b)

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