OC in circle O is perpendicular to ab AB = 16 sinaoc = 3 / 5 calculate radius OA of circle O and chord center distance OC calculate cosaoc tanaoc

OC in circle O is perpendicular to ab AB = 16 sinaoc = 3 / 5 calculate radius OA of circle O and chord center distance OC calculate cosaoc tanaoc

In △ AOC
sin∠AOC=AC/AO=3/5
And AC = AB / 2 = 8
Substituting
AO=40/3
The solution of Pythagorean theorem is OC = 32 / 3
cos∠COA=OC/AO=4/5
tan∠AOC=AC/OC=3/4