# Special Right Triangles Part 1: 45°-45°-90°

- Author:
- blanchal

- Topic:
- Right Triangles, Triangles

From a square we can draw a diagonal to create a 45°-45°-90° triangle. Is there anything special about the side lengths? Move the slider to change the side lengths of the square.

1. As you move the slider, record at least 3 different sets of side length values for segments AB, BC, and AC.
2. Using the three sets of side lengths you recorded, calculate sin(A), cos(A), and tan(A). Compare your sin, cos, and tan ratio values. Record any observations you have.
3. Using the three sets of side lengths you recorded, calculate sin(C), cos(C), and tan(C). Compare your sin, cos, and tan ratio values. Record any observations you have.
4. Compare your ratios in #2 to your ratios in #3. What do you notice?
5. What makes 45°-45°-90° triangles special?