Hi Zoe Lea
I think some of these replies may confuse you. Not because they're wrong - just a bit 'high level'.
I got an A in Maths two years ago - without ever mastering trigonometry. I do understand Pythagoras' theorem - which is why I recommend you master that first.
If you know the lengths of two sides of a right angled triangle, the theorem lets you work out the length of the third side. If you are told the length of all three sides, you can use the theorem to decide whether he triangle is indeed a right-angled triangle.
The theorem says that the square on the hypotenuse is equal to the sum of the squares on the other two sides. Unfortunately that doesnt mean much until it's explained!
Draw a horizontal line 4 cm long. From one end, draw a vertical line 3 cm long. You have drawn a right angle - and the two lines are called a and b.
Now draw a line from the end of a to the end of b. You have drawn a triangle. The third side is the longest side and it is called c or the hypotenuse. The hypotenuse is opposite the right angle.
The next step is to use each side of the triangle to draw 3 squares. The square with line a as the base has sides of length 4 cm (obviously) and the square with line b as its base has sides 3 cm long. How long is the hypotenuse ? Trust me, it's 5 cm. Draw the square with sides 5 cm long. If you covered each square with 'tiles' of 1 cm x 1 cm, you'd use:
16 to cover square a,
9 to cover square b,
25 to cover square c (the square on the hypotenuse ).
What have you just proved? That in a right-angled triangle with sides of 3, 4 and 5, the square of the hypotenuse (25) equals the sum of the squares of the other two sides (16 +9). Trust me, this is always true IF it's a right-angled triangle.
Once you really undestand and believe this rule, you have learned Pythagoras theorem.
Just remember 3, 4, 5. 9 + 16 = 25.
If the hypotenuse is 5 and one side is 4, then the other side must be 3.
Imagine a triangle with sides of 5, 6 and 9 cm. Is it a right-angled triangle ? No, it cant be, because:
5 x 5 = 25.
6 x 6 = 36.
9 x 9 = 81.
And 25 + 36 doesn't equal 81.
I hope this helps.