# Pythagoras and Trigonometry – Level J

## Pythagoras’ Theorem

### Proving Pythagoras’ Theorem

#### Instructions

How does Pythagoras’ Theorem work?

1. Redraw the diagram and label clearly.
2. Annotate the diagram with all you know about the lengths, angles, shapes and areas on the diagram.
3. Can you prove that c2 = a2 + b2?

## Trigonometry

### Triangle measurement

#### Instructions

Trigonometry literally means “triangle measurement”.

1. Measure the sides of your group of eight similar triangles (different sizes but same shape). What makes them similar?
2. Record your measurements in the table. Record the angle size of your triangles.
3. Calculate the ratios of each pair of sides (three sides means three pairs). Do you notice a pattern?
4. Calculate the mean (average) of the ratios. Share your results with the class and construct a graph of the ratios.
5. Use a calculator to find the sine, cosine and tangent (sin, cos, tan) of your angle size. What do you notice?
6. If the ratios for a certain angle size are always the same, we can use these relationships to find an unknown side or angle. Would you prefer to repeat this kind of triangle measurement or use a calculator?

### Use Trigonometry to calculate the size of things

Choose large objects around the school, measure sides and angles to calculate ‘unmeasurable’ sides and angles (at least one of each).