Question

已知山坡的坡角∠AEF=23°,量得树干倾斜角∠BAC=38°,大树被折断部分和坡面所成的角∠ADC=60°AD=4m

Answer 1

过D点做DG‖EF,做DH⊥DG

∴∠ADG=∠AEF=23°

∵AB⊥EF

∴DH‖AB

∴∠BAD+∠ADH=180°

∴∠BAD=180°-∠ADH

∵∠ADH=∠GDH-∠GDA=90°-23°=67°

∵∠CAD=∠BAD-∠BAC

∴∠CAE=∠CAD=180°-∠ADH-∠BAC=180°-67°-38°=75°

2.过A点做AO⊥CD

∵∠ADC=60°

∴∠OAD=30°

∵AD=4

∴OD=2,AO=2根号3=3.4

又∵∠CAE=75°

∴∠CAO=∠CAD-∠OAD=75°-30°=45°

∴CO=AO=3.4,CA=根号2AO=根号6OD=2.4*2=4.8

∴大树原高度=AC+CD=4.8+3.4+2=8.4