Introduction to Trigonometry
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!
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 |
As you can see, though the opposite side and hypotenuse values are changing, as long as
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
