Question

如图所示,在梯形ABCD中,AD‖BC,AB=5,AC=9,∠BCA=30°,∠ADB=45°.求BD的长.

Answer 1

因为AD‖BC

故：∠ABC+∠BAD=180°

因为AB=5,AC=9,∠BCA=30°,AB/sin∠BCA=AC/sin∠ABC

故：sin∠ABC=9/10

故：sin∠BAD=sin∠ABC=9/10

又：AB/sin∠ADB =BD/sin∠BAD,∠ADB=45°

故：BD=9√2/2