Pre Calculus I was disappointed in my students in their lack of connection with drawing right triangles for given angles.  Constructing a 30-60-90 triangle I would usually draw a generic triangle and label the angles.  I could be more specific for a 45-45-90 because the tangent ratio was 1 to 1.  Why not use other angles whose tangent ratios involved integers.  I created a list of such angles by using the inverse tangent function.  The students were much more comfortable even though the angles were "ugly."
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