If cos omega =
3
5
find tan omega

In triangle △abc, ∠abc=90°, bh is an altitude. find the missing lengths. ab=9, and ac=12, find hc.

Thee blue triangle has rotated from quadrant i to quadrant iii about the origin. describe the effects of the rotation on the coordinates of the blue triangle.

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.