In quadrilateral ABCD, we have ∠A = ∠C = 90◦ , ∠BDA = 2∠BDC, AB = 6, and AD = 8. Find the length of BC. (Diagram Below)
Hint: From Pythagorean Theorem, BD=10. Proceed to find the value of angle BDA from Law of Cosines (or Law of Sines, if you like that better) which gives you angle BDC. Then you have all of the angles in triangle BDC and one side, so use Law of Cosines to find BC.