Trigonometry

NZ Level 7 (NZC) Level 2 (NCEA)

Triangle Inequality (Investigation)

Lesson

- To explore the Triangle Inequality

- Colored straws (at least 7 different colors)
- Scissors
- Paper
- Pencil
- Ruler
- Protractor

- Measure and cut one straw into pieces 2 cm long.
- Measure and cut a different colored straw into pieces 3 cm long.
- Measure and cut a different colored straw into pieces 4 cm long.
- Measure and cut a different colored straw into pieces 5 cm long.
- Measure and cut a different colored straw into pieces 6 cm long.
- Measure and cut a different colored straw into pieces 7 cm long.
- Measure and cut a different colored straw into pieces 8 cm long.
- Measure and cut a different colored straw into pieces 10 cm long.
- Use the pieces of straw that you have cut out to create the following triangles and complete the table:

- Which attempts resulted in the creation of a triangle?
- For each of the attempts find the sum of the lengths of:
- Sides 2 and 3
- Sides 1 and 2
- Sides 1 and 3

- For the attempts that created triangles, compare each of the sums you found in the previous question to the remaining side not included in that sum. For example if I am looking at the sum of the lengths of sides 2 and 3 I would compare this number to the length of side 1. What do you notice?
- For the attempts that did not create triangles do the same thing. What do you notice?
- How is this different from the attempts that did create triangles?
- Based on your observations, what is a general rule you can make for the sides of a triangle?
- Compare your rule with a friend. Did they come to the same conclusion?
- With a partner, determine more combinations of side lengths that could create a triangle.
- Find the area of each of the triangles you were able to create throughout this entire investigation. Use a protractor if necessary.

Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions

Apply trigonometric relationships in solving problems