Question

如图,在△ABC中,AB=AC,AD⊥AB交BC于D,且∠CAD=30°,CD=4,求BC的长.

Answer 1

∵∠CAD=30° AD⊥AB ∴∠CAB=120°

∵AB=AC ∴∠B=∠C ∠B=∠C=(180°-∠CAB)/2=30°

∵∠CAD=30° ∠C=30° ∴∠CAD=∠C ∴CD=AD=4

∵AD⊥AB ∠B=30° ∴BD=2AD=8

BC=BD+CD=8+4=12