This is also two days worth of maths, we did: the four transformations ; Pythagoras’ theorem ; bearings ; trigonometry. Translation: the translation vector, how far it’s moved along the x-axis and how far it’s moved up or down the y-axis ; enlargement: the scale factor and the centre of enlargement or two things you need to know ; rotation: you need to know these things, angle turned, direction turned, centre of rotation ; reflection: you need to know where the mirror line is. Pythagoras’ theorem is this: A squared + B squared =H squared, it can only be used on right-angle triangles, here are the three steps:

- square the two numbers that you are given
- to find the longest side, add them and to find the shorter side, subtract them.
- take the square root and that your answer

There are three key points to a bearing:

- a bearing is the direction travelled between two points, given as an angle in degrees
- all bearings are measured clockwise from the north line
- all bearing should be given as 3 figures ( 045 not 45 or 009 not 9 )

After all that we talked about the method for solving right-angle triangles using SIN, COS, TAN:

- label the three sides O, A and H ( opposite, adjacent and hypotenuse )
- write down SOH CAH TOA
- decide which two sides are involved, O H , A H , O A
- turn the one you choose into a formula triangle
- cover up the thing you want to find
- translate into numbers and work it out
- finally check that you answer is sensible

the hypotenuse is the longest side, the opposite is the side opposite the angle being used and the adjacent is the side next to the angle being used. Here are a few things about the angle of depression and elevation:

- the angle of depression is the angles downwards from the horizontal
- the angle of elevation is the angle upwards from the horizontal
- the angle of elevation and depression equal each other

That’s all the maths we’ve done over the past couple of days, I understood most of it , but obviously, there is some stuff that went in one side of my brain and came straight out the other.