Question

Rt△ABC中，角C=90°，CD垂直AB于D，已知BD比AD＝1比4，求角B的正弦值和余弦值

Answer 1

设BD=a,则AD=4a
∵CD^2=BD*AD
∴CD=2a
∵CB^2=CD^2+BD^2
∴CB=√5a
sinB=CD/CB=2√5/5
cosB=BD/CB=√5/5

Answer 2

∵BC^2=BD·AB,AC^2=AD·AB
∴BD/AD=（BC/AC）^2
∴BC/AC=1/2
设BC=m,则AC=2m
∴AB=√5M
∴sinB=2√5/5,cosB=√5/5