- 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 30

and the side opposite the 60

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 45

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).

- Your Score Report appears after you have made 6 choices.

- Your Game Score is reduced by the number of butterfly hits.

- To slow the game speed repeat tap/click on the word

- To increase the game speed repeat tap/click on the word Math.

- Speed can also be adjusted with a keyboard's - and + keys.

- Refresh/Reload the web page to restart the game.

- Adjust the sound level of media on your device.

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