# Triangles and TrigonometryTrigonometry

So far we have seen relationships between the **angles** of triangles (e.g. they always sum up to 180°) and relationships between the **sides** of triangles (e.g. Pythagoras). But there is nothing that *connects* the size of angles and sides.

For example, if I know the three sides of a triangle, how do I find the size of its angles – without drawing the triangle and measuring them using a protractor? This is where **Trigonometry** comes in!

Imagine we have a right-angled triangle, and we also know one of the two other angles, **α**. We already know that the longest side is called the **hypotenuse**. The other two are usually called the **adjacent** (which is next to angle **α**) and the **opposite** (which is opposite angle **α**).

There are many different triangles that have angles **α** and 90°, but from the

Since all of these triangles are similar, we know that their sides are proportional. In particular, the following ratios are the same for all of these triangles:

Let’s try to summarise this: we picked a certain value for **α**, and got lots of similar, right-angled triangles. All of these triangles have the same ratios of sides. Since **α** was our only variable, there must be some relationship between **α** and those ratios.

These relationships are the **Trigonometric functions** – and there are three of them:

The three Trigonometric functions are relationships between the angles and the ratios of sides in a right-angles triangle. They each have a name, as well as a 3-letter abbreviation:

**Sine:**sin α = Opposite Hypotenuse **Cosine:**cos α = Adjacent Hypotenuse **Tangent:**tan α = Opposite Adjacent

COMING SOON – More on Trigonometry

## Inverse Trignometric Functions

COMING SOON – Inverse functions