Hello, I am the Greek mathematician Pythagoras.
I am going to talk to you about my theorem and how it works! Triangles are one of the most
Fundamental geometric shapes and I have a theorem that works like magic! If the triangle has a 90
degree angle, it can be used! It’s as simple as A squared + B squared = C squared. You will know the
triangle is a right-angled triangle if the square of the hypotenuse is equal to the sum of the squares
of the other two sides. To test this I want you all to draw a triangle and put for the ‘opposite’ side 4,
and for the adjacent side 3 and the hypotenuse 5.
25
16
5
4
3
9
Now for all of you who are not familiar with this theorem, some of your lovely hosts are going to
draw an example on the board, for you while I explain. Your 'opposite' side = 5, your opposite side is
the one which is opposite from the hypotenuse, your adjacent side = 12 which is other side opposite
from the hypotenuse and the hypotenuse side which is the longest side is unknown.
Write this down as we go along...
Draw a right-angled triangle; make sure you leave plenty of space. Draw a square on each side of the
triangle, if drawn on graph paper the picture is seen more clearly as you can see the amount of
squares it takes when you square each original side.
64
49
7
8
9
81
First you need to check if the areas are the same 7 squared + 9 squared = 8 squared, so 49 + 81 =
130. This is useful because if we know the lengths of two sides of a right angled triangle, we can find
the length of the third side. But this theorem only works on right-angled triangles.
Using my theorem, A squared + B squared = C squared you put 5 squared + 12 squared = C squared
as it is unknown to us at this stage. So first figure out what 5 squared equals, who knows the
answer? (25), then 12 squared who knows the answer (144) okay so next you will write 25 + 144 =
C2. Next you will add 25 + 144 which equals 169. So 169 = C2. Since c is squared you do that to the
169, so C = √169, and then you will get the end result, C = 13.
The 3 primary trigonometry functions are sine, cosine and tangent. These can be written sin, cos and
tan for short. We’re going to draw an example on the board for you, but for the answers you will
need a calculator.
Sin (A) = opposite / hypotenuse = 4.00 cm /
7.21 cm = 0.5548
Or simply: sin (A) = 0.5548
Now for the other two trig functions.
The value for the cosine of angle A is defined as the value that you get when you divide the adjacent
side by the hypotenuse. This can be written:
 cos(A) = a / h
Using the above measured triangle, this would mean that:
 cos(A) = adjacent / hypotenuse = 6.00 cm / 7.21 cm = 0.832
 cos(A) = 0.8322
The value for the tangent of angle A is defined as the value that you get when you divide the
opposite side by the adjacent side. This can be written:
 Tan (A) = opposite / adjacent
 Tan(A) = opp / adj
 Tan(A) = o / a
Using the above measured triangle, this would mean that:
 Tan (A) = opposite / adjacent = 4.00 cm / 6.00 cm = 0.6667
 Tan(A) = 0.6667
The angle A in the above triangle is actually very close to 33.7 degrees.
So, we would say:
 0.5548 = sin(33.7°)
 0.8322 = cos(33.7°)
 0.6667 = tan(33.7°)
If you wanted to know the trigonometry values for 47.5 degrees, you could carefully draw a right
triangle using a ruler and protractor that had an angle equal to 47.5 degrees in the position of angle
A. Then, you could carefully measure the sides. Lastly you could divide the appropriate sides to find
the values for the three trigonometric functions. You would find that:
 0.7373 = sin(47.5°)
 0.6755 = cos(47.5°)
 1.0913 = tan(47.5°)
Using the learning Object that has been chosen, you can go through the steps into assuring your
knowledge of the algebraic algorithms whilst having fun too. One of these lovely ladies will go
through the site and how you use it…