Pythagoras b h a a2 + b2 = h2

Pythagoras - Three simple steps Square the numbers of the sides you are given To find the longest side, add the two squared numbers. To find a shorter side, subtract the smaller squared number from the larger squared number. After adding or subtracting, take the square root. Then check that your answer is sensible.

Bearings 3 key points 1 A bearing is the direction travelled between two points, given as an angle in degrees 2 All bearings are measured clockwise from the northline (Marked N) 3 All bearings are given to 3 figures, e.g. 009, not 9 3 key words 1 “FROM”: Find the word from in question and pout your pencil on the diagram at the point you are going from. 2 At the point you are going from, draw in the northline. 3 Now draw in the angle clockwise from the northline to the line joining the two points. This angle is the bearing. A The bearing of A from B B N

Some Definitions A bearing is the direction travelled between two points, given as an angle in degrees All bearings are measured clockwise from the northline. All bearings should be given as 3 figures

Trigonometry: Using SIN, COS and TAN 7 steps for finding lengths of sides from angles 1. Label the sides, (o)pposite, (a)djacent and (h)ypotenuse How do you know how to which side to label what?? First ask:- What is the side opposite the side I have been given? Identify it and label it ‘opposite’ or ‘opp’, or just ‘o’. This has already been done in the diagram opposite. Then ask ‘Which side is adjacent to the angle that I have been given, which is not the longest side in the triangle? Identify it and label it ‘adjacent’, or ‘adj’ or ‘a’. This has already been done in the diagram opposite. Label the remaining (longest) side in the triangle ‘hypotenuse’, or ‘hyp’ or ‘h’. This has already been done in the diagram opposite. I have also labelled this side ‘x’ as I want you to find the length of this side in a little test at the end of this presentation. Labelling sides, example:- In this case, you have been given length of the opposite side (15cm). 35 o (15cm) h (x) a

Trigonometry: Using SIN, COS and TAN Formula triangles are:- Write down SOH CAH TOA from memory (these letters form the triangles in the diagram opposite) Decide which two sides are involved (How?) and select SOH, CAH, or TOA respectively, i.e. in this case the two sides involved are opposite and hypotenuse. These are the two underlined letters in SOH so its SOH you want! Why are these two sides involved?? – see next slide…

Trigonometry: Using SIN, COS and TAN Formula triangles are:- Turn the one that you want into a formula triangle (turn SOH into a formula triangle – this is the top one in the diagrams opposite). Cover up what you want to find - we want to find the length of the hypotenuse. So if you cover up H with your thumb you get the equation you need, i.e. O  S) Translate into numbers and work it out (i.e. 15  sin 35; see next slide for tips) Finally check you answer is sensible

How do you decide which sides are involved? Look for the side that you have been given the length of. This is one of the sides that is involved. The other side that is involved is the side that you have to find the length of. Decide which sides they are and go to the next slide (in this case I have already told you the sides involved are opposite and hypotenuse).

Calculator tips Try typing sin 30 into the calculator – you should get 0.5 if you are doing it right. From the previous slide we want 15 sin 35. Type this into calculator and see what your answer is. (26.15cm is correct!) In questions I will be setting you later on in tests you may be asked to calculate an angle in a triangle. In this case you will be given the lengths of two sides and using one of the formula triangles you will be able to calculate the angle - in our example it would be:- Inverse x Sin x (15/26.15) (= 35 degrees) !!

Loci and Constructions 7 different types of Loci – this is a revision list – you can read up them in your book The locus of points which are “A fixed Distance from a Given Point The locus of points which are “A fixed Distance from a Given Line” The locus of points which are “Equidistant from Two Given Lines” The locus of points which are “Equidistant from Two Given Points” Constructing accurate 60 angles Constructing accurate 90 angles Drawing a Perpendicular from a Point to a Line