In this interactive animation, you move the green point (C) at the top of the triangle. The two base points A (red) and B (purple) are fixed. When C moves, the angles change (between 0° and 180°) and at the same time the lines change. The relationships between all the lines change, becoming longer than, shorter than, half the length of, twice the length of etc. The relationship between the angles changes also. In a triangle, they share a total of 180°. In Maths, TRIGONOMETRY, is about the relationship between the sides and angles of triangles. LEARN BY DOING: Learn what is meant by the SINE of an angle from this project: (Remember, click the Stage to disconnect). 1. A triangle has three sides and three angles. 2. Each angle has two lines (or arms), and the angle is at the point (or vertex) where the lines meet. 3. In a triangle, the line that connects the two arms of an angle is said to be OPPOSITE the angle. 4. [In our animation] BC is opposite A, it's not part of the angle A. 5. The two arms of an angle are said to be ADJACENT to the angle that they form. 6. The line opposite a RIGHT-ANGLE (90°), has a special name, called a HYPOTENUSE. 7. [In our animation] The grey drop-line from C is perpendicular to AB (90°). It's not part of the triangle, but it makes AC a HYPOTENUSE. The grey line is opposite the angle at A. 8. SINE is a number, between -1 and 1. (Sine is neither an angle nor a line. It's a ratio.) 9. SINE is the ratio between the grey line (opposite A) and the hypotenuse. (Opposite / Hypotenuse) 10. The grey line is also opposite the angle at B, and it also makes BC a hypotenuse. Play around, move C and find the facts out for yourself.
To do 1: Drag to make a right-angle triangle with angles 90º, 30º, 60º. The length of the line opposite 30º is exactly ½ the length of the hypotenuse. The line opposite 60º is about 0.86 the length of the hypotenuse (From the picture draw that special triangle in your copybook) To do 2: Drag to make a triangle with angles 90º, 45º, 45º. The length of the line opposite the angle 45º is about 0.7 of the length of the hypotenuse. (Draw that special triangle in your copybook)
