Special Trigonometry Ratios for 30o,60o,45o Angles - Math Teaching Help - Game Tips: - A 60 degree angle is special since it is found in every equilateral triangle.    Splitting an equilateral triangle in half, yields two right triangles, each having 30, 60 & 90 degrees. - For each 30,60,90 right triangle, the sides have special ratios. Begin with hypotenuse length = 1 unit.    The side opposite the 30o angle is half the length of the side opposite the 90o angle    and the side opposite the 60o angle can be found from x2 + y2 = r2 , namely (1/2)2 + y2 = (1)2 .    So each 30,60,90 right triangle has sides in the special ratio 0.5 / 0.866 / 1.0 approx.    - Basic Trigonometry uses the ratios of the 'lengths of sides' of triangles as related to 'angle size'. - A 45 degree angle is also special since it is found twice in every right isosceles triangle. - For each 45,45,90 right triangle, the sides have special ratios. Use hypotenuse r=1.    A side opposite one 45o angle can be found from x2 + y2 = r2 , namely x2 + x2 = (1)2 .    So each 45,45,90 right triangle has sides in the special ratio 0.707 / 0.707 / 1.0 approx.    - When angle DAE is in standard position at a graph's origin (0,0) then sin A equals (y/r),    cos A equals (x/r), and tan A = (y/x). - When r=1 then the primary Trig ratios simplify to sin A = y,   cos A = x,   and tan A = (y/x). - It may take a minute to load the game at dial-up speeds. - The game can be played using the mouse by itself or using the keyboard by itself. - If the game doesn't respond to keyboard input, click inside the game area to reset the game's focus. - Adjust the game's speed by pressing the + or - key repeatedly.

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