trigonometry?

Question

in this:
http://tinyurl.com/2w3pxg
CD=5
BC=6
BE=3
angle D=angle C=90 degrees
calculate angle EOC

Answer 1

I am sorry that I do not know where is "O" for angle EOC. Anyway I can show you that all the segment lengths can be found, thus angle EOC can be found easily no matter where is "O".
Since CD = 5 and BC = 6, we can get BD = sqrt(11) by Pythagoras theorem.
BD*DA = CD*CD thus DA = 25/sqrt(11) = (25/11)sqrt(11), since triangles ADC similar to CDB. And AB = AD + BD = (36/11)sqrt(11).
Using Pythagoras theorem in ABC, AC can be found as (30/11)sqrt(11).
Using Pythagoras theorem in AEC, AE can be found as 3*sqrt(111/11).
Let the cross-section of AE and CD be P. Using mass-point method, we know CP/PD = 36/25, or CP/CD = 36/61, thus CP = 180/61 and PD = 125/61.
Also using mass-point method, we know AP/PE = 50/11, or AP/AE = 50/61, thus AP = (150/61)sqrt(111/11), and PE = (33/61)sqrt(111/11).