Question

设三角形ABC的内角A,B,C所对边的长分别是a,b,c,且b=3,c=1,A=2B.求a

设三角形ABC的内角A,B,C所对边的长分别是a,b,c,且b=3,c=1,A=2B.求a 哪位大神求求了？解解呗！今年高考题诶

Answer 1

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Answer 2

做∠BAC的平分线AD交BC于D ∵ ∠ADC=∠B+1/2∠A=2∠B=∠A ∠BAD=∠CAD=1/2∠A=∠B ∴ △ABC ∽△DAC AD=BD=BC - CD AD/AB=CD/AC AD/CD=AB/AC=1/3 CD=3AD=3BD BC=4BD AC/CD=BC/AC CD*BC=AC*AC 12BD²=9 BD=√(3/4)=√12/4 a = 4BD = √12