Click and drag the angle α to any value between 0° and 90°. Then click and drag b and b' to make any 2 right-triangles you want with angle α.
Look at first triangle: Divide the length of the side adjacent to the angle α by the length of the hypotenuse. Write this number down.
Look at the second triangle and again divide the lenth of the side adjacent to the angle α by the length of the hypotenuse. It should be the same number!
This is the value of cos(α).

Pick an angle α and find the cos(α) on this worksheet. Use the Move drawing pad tool to get an empty space on the worksheet. Then draw 2 points anywhere - not even on the same horizontal (but not too far apart ). Use these 2 points to draw a right-triangle with angle α . Divide the length of the side adjacent to α by the length of the hypotenuse of this triangle. You should get cos(α).