1. Working out an unknown side or angle in a right angled triangle. Miss Hudson’s Maths

2. The sides of a right angled triangle are named according to their position relative to the angle  Hypotenuse (Hyp) Opposite (Opp) Adjacent (Adj) Miss Hudson’s Maths

3. PRACTICE LABELING A TRIANGLE! Miss Hudson’s Maths

4. PRACTICE LABELING A TRIANGLE! Miss Hudson’s Maths

5. The sides are paired up to form the three ratios called sin, cos and tan (sine, cosine, tangent). SOHCAHTO A is often used to help remember these ratios (Hyp) (Opp) (Adj) SOHCAHTOA is used to help remember these ratios s o h a h ct o a O H A Miss Hudson’s Maths

6. METHOD: 1. Label sides with information on them as ‘O’, ‘A’ or ‘H’ 2. Use SOHCAHTOA to help choose which ratio to use: sin, tan or cos. 3. Write down the ratio 4. Put in the values from the question 5. Solve for the unknown side. O H eg 1: Find the length of the side labelled y y 10 cm 65° sin 65°= y = 9.06 cm (2dp) y = 10 x sin 65 10 x x 10 OH sin 65°= Miss Hudson’s Maths

7. eg 2: Find the length of the side k 78° k 3.2m O A tan 78°= x 3.2 3.2 x k = 3.2 x tan 78 k = 15.05 m (2dp) Make sure your calculator says ‘ D ’ and not ‘ R ’ or ‘ G ’ SOHCAHTOA eg 3: Find the length of the side labelled y A H cos 49° = y 5.6cm 49° x 5.6 5.6 x y = 5.6 x cos 49 y = 3.67 cm (2dp) OAAH tan 78°= cos 49° = Miss Hudson’s Maths

8. eg 4: Find the length of the side labelled p It ’ s not THAT hard Bart! 42° p 7.2 m sin 42° = O H Since the unknown is on the denominator, interchange as shown p = p = 10.76 m (2 dp) sin 42° = Miss Hudson’s Maths

9. METHOD: 1. Label sides with information on them as ‘O’, ‘A’ or ‘H’ 2. Use SOHCAHTOA to help choose which ratio to use: sin, tan or cos. 3. Write down the ratio 4. Put in the values from the question 5. Use SHIFT then the ratio to find the angle  7 cm 4 cm eg 1: Find the size of angle  A H AH cos  =  = cos -1 ( ) SHIFTCOS47a b /c=  = 55.2° (1 dp) To work out the angle use cos inverse, ie cos -1 cos  = Miss Hudson’s Maths

10. Angle of Elevation: This is the angle measured from the horizontal UP to something eg: angle of elevation Angle of Depression: This is the angle measured from the horizontal DOWN to something eg: angle of depression Miss Hudson’s Maths

11. VECTORS A vector is a quantity which has length and direction. A vector is described as where x is the distance across to the right (+) or left (-) and y is the distance up (+) or down (-) x y A vector is often labelled with a small letter, either in bold type or in ordinary type with a marking under it, ie a or a  eg: a = 4 1   eg: b = -2 -3 a  b  eg: c =  3 -5 c 

12. Adding Vectors To add vectors geometrically, we draw the 1 st vector and then draw the 2 nd vector starting at the end of the 1 st one. 4 1 3 -5 a  b  a + b   eg: If a = and b = then a + b is the shortest route from the very start to the end and is called the resultant.     a + b =   7 -4 NB: + = 4 1 3 -5 7 -4 + +

13. Multiplying Vectors If a =  1 2 then 3a = 3 1 2 = 3 x 1 3 x 2 = 3 6 a  3a  NB: 3a is 3 times as long as a and is parallel to it.  

14. Magnitude & Direction The direction of a vector is its angle. This is calculated using SOHCAHTOA. The magnitude of a vector is its length. It is written as, for example, |a| This is calculated using Pythagoras ’ Theorem.  eg: If b =  3 4 b  3 4 |b| 2 = 3 2 + 4 2  |b| 2 = 25  |b| = √25  |b| = 5  Let θ be the angle the vector makes with the horizontal. θ tan θ = θ = tan -1 ( ) θ = 53.1° (1 dp)  direction is 53.1° from the horizontal  length is 5 units