∵∠A:∠ABC:∠ACB=3:4:5
∴∠A=3*180/(3+4+5)=45°
∵CE⊥AB,BD⊥AC
∴∠AEC=90° ∠ADB=90°
∴∠EHD=360-90-90-45=135°
∵∠BHC=∠DHE
∴∠BHC=135°