You are given a right triangle ABC with angle ABC = 30 degrees and AB equal 7. Then AC and BC are then extended to points D and E so that EDC is a right triangle. Find length DE if BD = 15

First BC needs to be found. That is done by dividing AB by cosin ABC. Then CD is found by subtracting form BD. After that the angle ACB is 90-ABC (because ABC is right triangle). Then because AE and BD intersect at C, the angle ECD is equal to ACB. After that ED can either be found using sin, or by finding CDE and justify that both triangles are proportional (as they have all 3 same angles) and then ED is AB*CD/BC.