In this right angled triangle the hypotenuse is set to 1 unit. Notice how the green and red sides change in length when the angle gets smaller/larger.
What angle makes the green and red sides equal in length?
What angle makes the side adjacent to the angle (the red side) equal to 0.5?
As the angle increases in size, does the red side get longer or shorter?
As the angle increases in size, does the green side get longer or shorter?
When the angle is 20°, the green side is 0.342; the red side is 0.94. At what angle do they swap, that is, the red is 0.342 and the green is 0.94?
When the angle is 10°, the green side is 0.174; the red side is 0.985. At what angle do they swap, that is, the red is 0.174 and the green is 0.985?
When the angle is 5°, the green side is 0.087; the red side is 0.996. At what angle do they swap, that is, the red is 0.0.087 and the green is 0.996?
What is the relationship between the two angles in the previous three questions? (The two angles that make the green and red sides swap lengths).
What does the Pythagorean theorem say about the green side, the red side and the number 1,for any angle? Give an example.
Suppose a right angled triangle has hypotenuse length 5 cm, and one of the angles is 23°. Use the applet above to figure out how long the other two sides would be.