What is the ratio of sides for a 30°-60°-90° triangle and what is the reference angle for 225°?

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flbyrne | (Level 3) Assistant Educator

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A 30-60-90 triangle is one of the standard right triangles and the ratio of its sides is:

1:2:`sqrt3`

The smallest angle (30 degrees) is opposite to the smallest side (1) and the largest angle (90 degrees) is opposite to the largest side (2). It would make more sense to write the ratio as 1:`sqrt3` :2, but 1:2:`sqrt3` is easier to remember.

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A reference angle is the smallest angle that the terminal side of a given angle makes with the x axis.

Determine in which quadrant is 225 degrees. The first quadrant goes from 0 to 90 degrees, the second quadrant goes from 90 to 180 degrees, the third quadrant goes from 180 to 270 degrees. Therefore 225 is in the third quadrant.

In order to determine the reference angle, subtract 180 degrees (the closest side of the x axis) from 225 degrees.

`225-180=45`o

Therefore the reference angle for ` `225 degrees is 45 degrees.

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