This is a right triangle or R.A.T (right angled triangle). The longest part of the triangle is called the hypotenuse (hypotenuse = c). The legs are what create the 90 degree angle. The letters used for the legs are a and b, and it doesn't matter which line you put a or b on. The square at the corner of the right triangle tells you that it's a 90 degree angle. The sign that looks like a circle with a line through it is called theta and the the sign that looks like the letter b is called beta.
This is a square. Squares a quadrilaterals. You can tell that the the square's side are all equal because of the line on each side of the squares. Again, the squares at the corners tell you that it's at a 90 degree angle. The internal angle of the square is 360 degrees (90 x 4 = 360).
This is the formula for the Pythagorean Theorem. Pythagoras was able to prove this formula using the right triangle, and the squares.
This mystery man is named Pythagoras. He was a Greek teacher and philosopher. Pythagoras calculated the circumference of the earth and realized that the earth is a sphere. He is also a vegetarian. Pythagoras discovered the Pythagorean Theorem (a² + b² = c²). Picture taken from Mr. Harbeck's blog post.
Problem 1
In this problem, we have to find out what the letter b is. We know that a = 8, and c = 10. So this is how it starts :
a² + b² = c²
8² + b² = 10²
Now, to isolate b², we add negative 8² to both sides:
8² -8² + b² = 10² - 8²
b² = (10x10) - (8x8)
b² = 100 - 64
b² = 36
Then, to isolate the b, we square root. We do the same thing to the 36 :
b = 6
But we're not done yet! Since there are 2 triangles in one, we're figuring out the b for both of them. So:
b + b
6 + 6 = 12
So the b for the whole triangle is 12 mm!
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? Giver your answer to the nearest tenth of centimetre.
In this problem, we have to find out what the letter c is. We know that a = 3, and c = 3. So this is how it starts :
a² + b² = c²
3² + 3² = c²
Then we'll make it look easier by doing this:
(3 x 3) + (3 x 3) = c²
Then we solve it:
9 + 9 = c²
18 = c²
4.2 cm = c
B) What is the length of the diagonal of the board? Give your answer to the nearest centimetre.
In this problem, we have to find out what the letter c is. We know that a = 8, and b = 8. So this is how it starts :
a² + b² = c²
8² + 8² = c²
Then we'll make it look easier by doing this:
(8 x 8) + (8 x 8) = c²
Then we solve it:
64 + 64 = c²
128 = c²
11.3 = c
Pythagoras Theorem from Abby Sarao on Vimeo.
How To Find B from Abby Sarao on Vimeo.
0 comments:
Post a Comment