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This Exploration demonstrates that an angle has a constant sine, cosine, and tangent ratio.
Instructions
Click the button "Lab 3.2".
A right triangle ABC appears which has a red dot at B and a blue dot at C. The size of the angle CAB is 34.7o, and the length of AB, AC, and BC are 217, 263.8, and 150 units respectively.
The value for the sine, cosine, and tangent ratios are given in the top left corner.
The triangle can be resized by using the mouse to point at a dot and then clicking and draging the dot to a new position.
Answer the questions below.
- Click-and-drag the red dot horizontally so that the triangle is made smaller or larger without changing the size of the angle CAB (approximately). Watch the size of the sides of the triangle and the corresponding ratios.
(a) What name do we give to each of the different triangles produced?
(b) Write a sentence explaining what happens to the sine, cosine, and tangent ratios as the size of the triangle changes (approximately).
- Click-and-drag the blue dot vertically to change the size of angle CAB.
(a) Repeat question 1 above for the new angle.
(b) Write a sentence explaining what happens to the sine, cosine, and tangent ratios for different angles in a right triangle.
- Repeat question 2 to complete the table below, so that you have a record of the ratios for each value of the angle CAB.
| Angle CAB(degrees) | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
| Sine | | | | | | | | |
| Cosine | | | | | | | | |
| Tangent | | | | | | | | |
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