Trigonometry
Key Terms
Adjacent = Next to or joining something else.
Denominator = The bottom number in a fraction. Function = a relation or expression involving one or more variables. Hypotenuse = The longest side of a triangle. Inverted = Turned up side down. Numerator = The top number of the fraction. Opposite = situated on the other or further side when seen from a specified place. 
Right angle = An angle that is exactly 90 degrees.
Squared = A number multiplied by itself. Substitute = To swap something. Trig Value = are functions of an angle Trigonometrical ratio = the ratios relate the sides of a right triangle to its angles. Vertical = Straight up line 
SohCahToa and labelling triangles.
SohCahToa, is the mathematical term given to working out which trig value you use when working out the length or an angle in a triangle. The S stands for Sine(sin), the C stands for Cosine (Cos) and the T stands for Tangent (Tan). Then the letters after each represent which sides are present. The three sides are labelled as follows:

The longest side  Hypotenuse (Right angles triangle it is opposite the 90 degree angle) (H)
The angle opposite the angle you want to find  Opposite (O)
The angle that runs off the angle you want to find  Adjacent (A)
Toa means Opposite over Adjacent. if you are trying to find an angle you would do the opposite divided by the adjacent times tan or Tan 1 on the calculator. To find the side you time the angle by your side Tan (angle) x opposite or hypotenuse.
Soh means Opposite over hypotenuse. To find the angle its Sin1(ans) and when finding the side you use Sin(angle).
Cah means Adjacent over hypotenuse and the trig function of Cos or Cosine.
The angle opposite the angle you want to find  Opposite (O)
The angle that runs off the angle you want to find  Adjacent (A)
Toa means Opposite over Adjacent. if you are trying to find an angle you would do the opposite divided by the adjacent times tan or Tan 1 on the calculator. To find the side you time the angle by your side Tan (angle) x opposite or hypotenuse.
Soh means Opposite over hypotenuse. To find the angle its Sin1(ans) and when finding the side you use Sin(angle).
Cah means Adjacent over hypotenuse and the trig function of Cos or Cosine.
Pythagoras Theorem

Pythagoras theorem is what is used to work out the sides of a right angled triangle. Pythagoras theorem is C squared = A squared + B squared. This is basically the Vertical times by itself side add the bottom side times by itself is equal to the longest side. For example if A = 3 B = 4 this would make C = 5 this is because 3 squared is 9, 4 squared 16 which adds to get 25. The square root is 5.

Trig Ratios.
Sine Rule.

The Sine Rule applies to triangles that are non right angled and when you are given 3 elements that include two angles and a side. Or 2 sides and an angle. However these need to be the angle given needs to be opposite the side you are given. Then the remaining side or angle needs to be opposite what you have. When using the sine rule it can be written in two ways, the first is when working out a side, which is the equation above. However this can be inverted when trying to work out a an angle.

To start off with you need to label the angles A, B and C, it doesn't really matter which ones you label A,B and C but it is easier to work with these rather than the random letters you are normally given. Then label the sides opposite each angle with a lower case letter of the angle. For example: The side opposite angle A would be side a. Next you substitute the letters into the formula with the angles being placed next to the Sine part. For Example if angle A was 40 I would put sine 40 under side a. Then you divide the numerator by the denominator. You then times this by the remaining value. If you are trying to find an angle you have to inverse sin your answer. This is the function on the calculator that appears as sin to the 1 power. Below there is an example of when you find an angle and when you find a side:
Cosine Rule.
To work out the Cosine rule you need 3 sides and no angle or 2 sides and angle that is opposite the side you are trying to work out. To find the unknown angle you square both the given angles, subtract the two angles times multiplied by Cos of the side. See the examples below:
1. Find the angle, 2. Find the side, 

Area of a triangle.

A triangles vertical height is the point from the base of the triangle (The bottom) to the tip of the triangle. The this line goes straight up from the highest point straight to the bottom and is normally shown with a dotted line. At the start of the question you should draw this line the triangle is split into two right angle triangles. To work out the area you multiply angles a and b. Then times this number by sin c which is the sine of the side given, then half this answer by 2 to get the answer.

Related Resources
This topic is covered by the Code Ma.13. and there are resources available in the THS store for this topic. Student worksheets are free and we have a range of quality lessons available for purchase, these include lesson plans, activity's and presentations for each lesson.
