# Trigonometry

```Trigonometry
Trigonometry is the study of the relationships between the sides and angles of
triangles. More specifically, right triangles. Trigonometry has its origins in
astronomy (i.e. measuring the distance to the moon). These ratios were
discovered by the mathematician Hipparchus and the astronomer Ptolemy.
1. Are these three triangle similar? How do you know (what post/theorem)?
2. What do you observe about angle A, angle B, and angle C?
3. Use the above right triangles to calculate the following ratios (write the
fraction and then round to the nearest tenth):
Triangle 1
Triangle 2
Triangle 3
Leg opposite &lt;A
Leg opposite &lt;B
Leg opposite &lt;C
Hypotenuse
Hypotenuse
Hypotenuse
Leg opposite &lt;A
Hypotenuse
Leg opposite &lt;B
Hypotenuse
Leg opposite &lt;C
Hypotenuse
4. Now on your calculator, locate the sin, cos, and tan keys. Use your
calculator to find the following answers:
tan 31 =
cos 31 =
sin 31 =
5. What do you notice? (Think hard, you’ll share this with the class)
```