| Right-angled triangles | Non right-angled
triangles (higher maths only) |
||
| To find one side using the lengths of the other two sides, use Pythagoras | If you need to use an angle in the calculation, use sin, cos or tan | For some triangles, use sine rule | For other triangles, use cosine rule |
In a right angle triangle, c2 = a2 + b2, where c is the length of the the hypotenuse and a and b are the lengths of the other two sides (which enclose the right angle).
With some (but not most) right angle triangles, a, b and c are whole numbers. A Pythagorean triple is a set of three whole numbers that form the sides of a right-angled triangle.
The most common case of this is when a = 3, b = 4 and c = 5. A triangle with this exact shape is called a 3,4,5 triangle. You should be able to spot a 3,4,5 triangle.
(Check this: c2 = a2 + b2 = 32 + 42 = 25. So c = √25 = 5. Note: the symbol √ means 'square root of')
(A triangle with sides of length 6, 8 and 10 is also a 3,4,5 triangle since it has the same shape, with its sides being twice the length.)
(Another example of a pythagorean triple is {5,12,15}.
This bit is NOT on the GCSE syllabus, but it's good practice --> you can use Pythagoras' Theorem to find the distance between two points if you know their co-ordinates. In the diagrams below, you can just see the grids, which allow you to count the units in the x and y directions.
sin θ = opp / hyp cos θ = adj / hyp tan θ = opp / adj |
opp is short for opposite |