# Introduction to Trigonometry

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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 sizes 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!

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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**).

Let us look at the below 4 right angle triangles.

Figure 1

Figure 2

Figure 3

Figure 4

Please fill up the values in the below table based on the images above:

Figure No. | Angle( | Opposite Side | Hypotenuse | |
---|---|---|---|---|

1 | 30 | |||

2 | 30 | |||

3 | 30 | |||

4 | 30 |

Let us conclude from the above values.

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As you can see, though the opposite side and hypotenuse values are changing, as long as **30 ^{o}** the ratio of

**always remains as**opposite side hypotenuse

**or**1 2

**0.5**.

Experiment with different triangles and see if this holds. Experiment to see if the ratio of different sides: (

There are many different triangles that have angles **α** and 90°, but from the AA condition we know that they are all

Let's see some trigonometric ratios.