1、∵MN⊥AB于N且平分AB,交AC于M
∴BM=AM
∴∠A=∠MBA=15°
∵∠ABC=90°-∠A=90°-15°=75°
∴∠MBC=∠ABC-∠MBA=75°-15°=60°
∵∠C=90°
∴∠CMB=90°-∠MBC=90°-60°=30°
∴BC=1/2BM=1/2AM
2、BC=AB×sjn15°=8×(√6-√2)/4=2√6-2√2
AC=AB×cos15°=8×(√6+√2)/4=2√6+2√2
∴S△ABC
=1/2AC×BC
=1/2×(2√6+2√2)(2√6-2√2)
=1/2×(24-8)
=8